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Senthilvelan, Murugaian

Author ID: senthilvelan.murugaian Recent zbMATH articles by "Senthilvelan, Murugaian"
Published as: Senthilvelan, M.; Senthil Velan, M.; Senthilvelan, Murugaian; Velan, M. Senthil
Homepage: http://www.bdu.ac.in/schools/physics/non-linear-dynamics/docs/faculty/dr_m_senth...
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Publications by Year

Citations contained in zbMATH Open

86 Publications have been cited 814 times in 485 Documents Cited by Year
On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations. Zbl 1186.34046
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
54
2005
A nonlinear oscillator with quasi-harmonic behaviour: two- and \(n\)-dimensional oscillators. Zbl 1068.37038
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano; Senthilvelan, Murugaian
53
2004
On the extended applications of homogeneous balance method. Zbl 1032.35159
Senthilvelan, M.
52
2001
A simple and unified approach to identify integrable nonlinear oscillators and systems. Zbl 1111.34003
Chandrasekar, V. K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
44
2006
Classification of Lie point symmetries for quadratic Liénard type equation \(\ddot{x}+f(x)\dot{x}^2+g(x)=0\). Zbl 1295.34049
Tiwari, Ajey K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
26
2013
New aspects of integrability of force-free Duffing-van der Pol oscillator and related nonlinear systems. Zbl 1069.34055
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
22
2004
A group theoretical identification of integrable equations in the Liénard-type equation \(\ddot x+f(x)\dot x+g(x) = 0\). II: Equations having maximal Lie point symmetries. Zbl 1283.34036
Pandey, S. N.; Bindu, P. S.; Senthilvelan, M.; Lakshmanan, M.
22
2009
On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator. Zbl 1137.70344
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
20
2007
A unification in the theory of linearization of second-order nonlinear ordinary differential equations. Zbl 1146.34312
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
20
2006
On the general solution for the modified Emden-type equation \(\ddot x+\alpha x\dot x+\beta x^3=0\). Zbl 1128.34003
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
19
2007
Nonstandard bilinearization of \(\mathcal{PT}\)-invariant nonlocal nonlinear Schrödinger equation: bright soliton solutions. Zbl 1378.35074
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
19
2017
A nonlocal connection between certain linear and nonlinear ordinary differential equations/ oscillators. Zbl 1107.34003
Chandrasekar, V. K.; Senthilvelan, M.; Kundu, Anjan; Lakshmanan, M.
17
2006
Lie symmetries, Kac-Moody-Virasoro algebras and integrability of certain \((2+1)\)-dimensional nonlinear evolution equations. Zbl 1119.37324
Senthil Velan, M.; Lakshmanan, M.
16
1998
On the complete integrability and linearization of nonlinear ordinary differential equations. II: Third-order equations. Zbl 1149.34319
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
16
2006
A group theoretical identification of integrable cases of the Liénard-type equation \(\ddot x +f(x)\dot x +g(x)=0\). I: Equations having nonmaximal number of Lie point symmetries. Zbl 1328.34031
Pandey, S. N.; Bindu, P. S.; Senthilvelan, M.; Lakshmanan, M.
14
2009
Generalized Darboux transformation and \(N\)th order rogue wave solution of a general coupled nonlinear Schrödinger equations. Zbl 1334.37084
Vishnu Priya, N.; Senthilvelan, M.
14
2015
Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation. Zbl 1115.37347
Kraenkel, R. A.; Senthilvelan, M.; Zenchuk, A. I.
13
2000
Nonstandard conserved Hamiltonian structures in dissipative/damped systems: nonlinear generalizations of damped harmonic oscillator. Zbl 1187.34046
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
13
2009
Extended Prelle-Singer method and integrability/solvability of a class of nonlinear \(n\)th order ordinary differential equations. Zbl 1362.34002
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
12
2005
On the construction of coherent states of position dependent mass Schrödinger equation endowed with effective potential. Zbl 1310.81054
Chithiika Ruby, V.; Senthilvelan, M.
12
2010
Exact quantization of a PT-symmetric (reversible) Liénard-type nonlinear oscillator. Zbl 1252.81055
Ruby, V. Chithiika; Senthilvelan, M.; Lakshmanan, M.
12
2012
On symmetry preserving and symmetry broken bright, dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation. Zbl 1404.35422
Vishnu Priya, N.; Senthilvelan, M.; Rangarajan, Govindan; Lakshmanan, M.
11
2019
Energy-sharing collisions and the dynamics of degenerate solitons in the nonlocal Manakov system. Zbl 1432.37092
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
10
2019
On the nonlocal symmetries of certain nonlinear oscillators and their general solution. Zbl 1250.34030
Bruzon, M. S.; Gandarias, M. L.; Senthilvelan, M.
10
2011
On the solutions of the position-dependent effective mass Schrödinger equation of a nonlinear oscillator related with the isotonic oscillator. Zbl 1179.81057
Kraenkel, R. A.; Senthilvelan, M.
10
2009
Application of extended Prelle–Singer procedure to the generalized modified Emden type equation. Zbl 1086.34500
Chandrasekar, V. K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
9
2005
Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I symmetry preserving and symmetry breaking solutions. Zbl 1439.35447
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
9
2019
Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger equation. Zbl 07412670
Sinthuja, N.; Manikandan, K.; Senthilvelan, M.
9
2021
Direct integration of generalized Lie or dynamical symmetries of three degrees of freedom nonlinear Hamiltonian systems: Integrability and separability. Zbl 0784.58053
Lakshmanan, M.; Velan, M. Senthil
8
1992
Lie symmetries and invariant solutions of the shallow-water equation. Zbl 0864.76018
Velan, M. Senthil; Lakshmanan, M.
8
1996
Dynamics of a completely integrable \(N\) coupled Liénard-type nonlinear oscillator. Zbl 1182.70025
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2009
Lie symmetries and infinite-dimensional Lie algebras of certain nonlinear dissipative systems. Zbl 0833.34037
Senthil Velan, M.; Lakshmanan, M.
8
1995
Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation. Zbl 1089.81019
Senthilvelan, M.; Torrisi, M.; Valenti, A.
8
2006
Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations. Zbl 1359.34004
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2014
Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators. Zbl 1308.81074
Chithiika Ruby, V.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2015
On the complete integrability of a nonlinear oscillator from group theoretical perspective. Zbl 1276.81050
Bhuvaneswari, A.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2012
On certain new exact solutions of a diffusive predator-prey system. Zbl 1261.35143
Kraenkel, R. A.; Manikandan, K.; Senthilvelan, M.
8
2013
On the integrable perturbations of the Camassa-Holm equation. Zbl 1052.37058
Kraenkel, R. A.; Senthilvelan, M.; Zenchuk, A. I.
7
2000
Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems. Zbl 1131.34030
Bluman, George; Cheviakov, Alexei F.; Senthilvelan, M.
7
2008
Nonlocal symmetries of Riccati and Abel chains and their similarity reductions. Zbl 1274.34020
Bruzon, M. S.; Gandarias, M. L.; Senthilvelan, M.
7
2012
Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator. Zbl 1373.81201
Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.
7
2017
Multi-loop soliton solutions and their interaction in the Degasperis-Procesi equation. Zbl 1298.37058
Stalin, S.; Senthilvelan, M.
7
2012
On the complete integrability and linearization of nonlinear ordinary differential equations. III. Coupled first-order equations. Zbl 1186.34048
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
7
2009
On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations. Zbl 1454.35353
Vishnu Priya, N.; Senthilvelan, M.
6
2015
Symmetry analysis of an integrable reaction-diffusion equation. Zbl 1015.35006
Kraenkel, R. A.; Senthilvelan, M.
6
2001
Stable amplitude Chimera states in a network of locally coupled Stuart-Landau oscillators. Zbl 1390.34148
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2018
N-bright-bright and N-dark-dark solitons of the coupled generalized nonlinear Schrödinger equations. Zbl 1470.35340
Vishnu Priya, N.; Senthilvelan, M.
6
2016
Lie point symmetries classification of the mixed Liénard-type equation. Zbl 1437.34039
Tiwari, Ajey K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
6
2015
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system. Zbl 1309.34007
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2010
A nonlocal connection between certain linear and nonlinear ordinary differential equations: extension to coupled equations. Zbl 1314.34034
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2010
On the generalized intelligent states and certain related nonclassical states of a quantum exactly solvable nonlinear oscillator. Zbl 1200.81084
Ruby, V. Chithiika; Senthilvelan, M.
6
2010
On the complete integrability and linearization of nonlinear ordinary differential equations. V. Linearization of coupled second-order equations. Zbl 1186.34050
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2009
Application of the \(\lambda\)-symmetries approach and time independent integral of the modified Emden equation. Zbl 1239.34002
Bhuvaneswari, A.; Kraenkel, Roberto A.; Senthilvelan, Murugaian
5
2012
Direct integration of generalized Lie symmetries of nonlinear Hamiltonian systems with two degrees of freedom: Integrability and separability. Zbl 0760.35050
Lakshmanan, M.; Senthil Velan, M.
5
1992
Ladder operators and squeezed coherent states of a three-dimensional generalized isotonic nonlinear oscillator. Zbl 1275.81052
Ruby, V. Chithiika; Karthiga, S.; Senthilvelan, M.
5
2012
On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations. Zbl 1186.34049
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
5
2009
Erratum: “Classification of Lie point symmetries for quadratic Liénard type equation \(\ddot{x}+f(x)\dot{x}^2+g(x)=0\)”. Zbl 1318.34052
Tiwari, Ajey K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
5
2014
Lie symmetries, infinite-dimensional Lie algebras and similarity reductions of certain \((2+1)\)-dimensional nonlinear evolution equations. Zbl 1044.37546
Lakshmanan, M.; Senthil Velan, M.
4
1996
Potential symmetries and new solutions of a simplified model for reacting mixtures. Zbl 0987.76099
Senthilvelan, M.; Torrisi, M.
4
2000
A note on the prolongation structure of the cubically nonlinear integrable Camassa-Holm type equation. Zbl 1254.76029
Stalin, S.; Senthilvelan, M.
4
2011
An inclusive SUSY approach to position dependent mass systems. Zbl 1396.81200
Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.
4
2018
Deformation of dark solitons in a \(\mathcal{P} \mathcal{T}\)-invariant variable coefficients nonlocal nonlinear Schrödinger equation. Zbl 1396.35057
Manikandan, K.; Vishnu Priya, N.; Senthilvelan, M.; Sankaranarayanan, R.
4
2018
Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order. Zbl 1236.34044
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
3
2011
A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator. Zbl 1245.81055
Ruby, V. Chithiika; Senthilvelan, M.
3
2012
An analysis of spatiotemporal localized solutions in the variable coefficients \((3 + 1)\)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters. Zbl 1375.35502
Manikandan, K.; Senthilvelan, M.
3
2016
A note on the Painlevé analysis of a \((2+1)\)-dimensional Camassa-Holm equation. Zbl 1099.35097
Gordoa, P. R.; Pickering, A.; Senthilvelan, M.
2
2006
Singularity structure, symmetries and integrability of generalized Fisher-type nonlinear diffusion equation. Zbl 0992.35077
Bindu, P. S.; Senthilvelan, M.; Lakshmanan, M.
2
2001
On certain new solutions of a simplified model for reacting mixtures. Zbl 1012.76100
Senthilvelan, M.; Torrisi, M.
2
2002
Reply to ‘Comment on “On the general solution for the modified Emden type equation \(\ddot{x}+\alpha x\dot x+\beta x^3=0\)”’. Zbl 1137.34301
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2008
On the interconnections between various analytic approaches in coupled first-order nonlinear differential equations. Zbl 1470.34102
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2018
On the linearization of isochronous centre of a modified Emden equation with linear external forcing. Zbl 1457.34048
Mohanasubha, R.; Sabiya Shakila, M. I.; Senthilvelan, M.
2
2014
Dynamical behaviour of solitons in a \(\mathcal{P} \mathcal{T} \)-invariant nonlocal nonlinear Schrödinger equation with distributed coefficients. Zbl 1515.35255
Manikandan, Kannan; Stalin, Seenimuthu; Senthilvelan, Murugaian
2
2018
Higher-order matter rogue waves and their deformations in two-component Bose-Einstein condensates. Zbl 1501.76004
Manikandan, K.; Vishnu Priya, N.; Senthilvelan, M.; Sankaranarayanan, R.
2
2022
Interconnections between various analytic approaches applicable to third-order nonlinear differential equations. Zbl 1371.34046
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2015
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations. I: Scalar case. Zbl 1255.34038
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2012
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations. II: Extension to coupled ODEs. Zbl 1255.34039
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2012
An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator. Zbl 1278.81070
Ruby, V. Chithiika; Senthilvelan, M.
2
2012
Lie point symmetries and the time-independent integral of the damped harmonic oscillator. Zbl 1263.70024
Bhuvaneswari, A.; Kraenkel, R. A.; Senthilvelan, M.
2
2011
Invariance analysis of the \((2+1)\)-dimensional long dispersive wave equation. Zbl 0952.35005
Senthil Velan, M.; Lakshmanan, M.
1
1997
On the integrability, Bäcklund transformation and symmetry aspects of a generalized Fisher type nonlinear reaction-diffusion equation. Zbl 1061.35037
Bindu, P. S.; Lakshmanan, M.; Senthilvelan, M.
1
2004
On the role of four-wave mixing effect in the interactions between nonlinear modes of coupled generalized nonlinear Schrödinger equation. Zbl 1429.35181
Vishnu Priya, N.; Senthilvelan, M.; Rangarajan, Govindan
1
2019
The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective. Zbl 1358.70022
Tiwari, Ajey K.; Pandey, S. N.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
1
2016
Similarity reductions of peakon equations: integrable cubic equations. Zbl 1511.35088
Barnes, L. E.; Hone, A. N. W.; Senthilvelan, M.; Stalin, S.
1
2022
Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains. Zbl 1470.34110
Gladwin Pradeep, R.; Chandrasekar, V. K.; Mohanasubha, R.; Senthilvelan, M.; Lakshmanan, M.
1
2016
A nonlocal connection between certain linear and nonlinear ordinary differential equations. II: Complex nonlinear oscillators. Zbl 1334.34085
Mohanasubha, R.; Sheeba, Jane H.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
1
2013
The Prelle-Singer method and Painlevé hierarchies. Zbl 1305.37036
Gordoa, P. R.; Pickering, A.; Senthilvelan, M.
1
2014
Higher-order matter rogue waves and their deformations in two-component Bose-Einstein condensates. Zbl 1501.76004
Manikandan, K.; Vishnu Priya, N.; Senthilvelan, M.; Sankaranarayanan, R.
2
2022
Similarity reductions of peakon equations: integrable cubic equations. Zbl 1511.35088
Barnes, L. E.; Hone, A. N. W.; Senthilvelan, M.; Stalin, S.
1
2022
Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger equation. Zbl 07412670
Sinthuja, N.; Manikandan, K.; Senthilvelan, M.
9
2021
On symmetry preserving and symmetry broken bright, dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation. Zbl 1404.35422
Vishnu Priya, N.; Senthilvelan, M.; Rangarajan, Govindan; Lakshmanan, M.
11
2019
Energy-sharing collisions and the dynamics of degenerate solitons in the nonlocal Manakov system. Zbl 1432.37092
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
10
2019
Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I symmetry preserving and symmetry breaking solutions. Zbl 1439.35447
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
9
2019
On the role of four-wave mixing effect in the interactions between nonlinear modes of coupled generalized nonlinear Schrödinger equation. Zbl 1429.35181
Vishnu Priya, N.; Senthilvelan, M.; Rangarajan, Govindan
1
2019
Stable amplitude Chimera states in a network of locally coupled Stuart-Landau oscillators. Zbl 1390.34148
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2018
An inclusive SUSY approach to position dependent mass systems. Zbl 1396.81200
Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.
4
2018
Deformation of dark solitons in a \(\mathcal{P} \mathcal{T}\)-invariant variable coefficients nonlocal nonlinear Schrödinger equation. Zbl 1396.35057
Manikandan, K.; Vishnu Priya, N.; Senthilvelan, M.; Sankaranarayanan, R.
4
2018
On the interconnections between various analytic approaches in coupled first-order nonlinear differential equations. Zbl 1470.34102
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2018
Dynamical behaviour of solitons in a \(\mathcal{P} \mathcal{T} \)-invariant nonlocal nonlinear Schrödinger equation with distributed coefficients. Zbl 1515.35255
Manikandan, Kannan; Stalin, Seenimuthu; Senthilvelan, Murugaian
2
2018
Nonstandard bilinearization of \(\mathcal{PT}\)-invariant nonlocal nonlinear Schrödinger equation: bright soliton solutions. Zbl 1378.35074
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
19
2017
Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator. Zbl 1373.81201
Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.
7
2017
N-bright-bright and N-dark-dark solitons of the coupled generalized nonlinear Schrödinger equations. Zbl 1470.35340
Vishnu Priya, N.; Senthilvelan, M.
6
2016
An analysis of spatiotemporal localized solutions in the variable coefficients \((3 + 1)\)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters. Zbl 1375.35502
Manikandan, K.; Senthilvelan, M.
3
2016
The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective. Zbl 1358.70022
Tiwari, Ajey K.; Pandey, S. N.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
1
2016
Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains. Zbl 1470.34110
Gladwin Pradeep, R.; Chandrasekar, V. K.; Mohanasubha, R.; Senthilvelan, M.; Lakshmanan, M.
1
2016
Generalized Darboux transformation and \(N\)th order rogue wave solution of a general coupled nonlinear Schrödinger equations. Zbl 1334.37084
Vishnu Priya, N.; Senthilvelan, M.
14
2015
Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators. Zbl 1308.81074
Chithiika Ruby, V.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2015
On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations. Zbl 1454.35353
Vishnu Priya, N.; Senthilvelan, M.
6
2015
Lie point symmetries classification of the mixed Liénard-type equation. Zbl 1437.34039
Tiwari, Ajey K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
6
2015
Interconnections between various analytic approaches applicable to third-order nonlinear differential equations. Zbl 1371.34046
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2015
Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations. Zbl 1359.34004
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2014
Erratum: “Classification of Lie point symmetries for quadratic Liénard type equation \(\ddot{x}+f(x)\dot{x}^2+g(x)=0\)”. Zbl 1318.34052
Tiwari, Ajey K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
5
2014
On the linearization of isochronous centre of a modified Emden equation with linear external forcing. Zbl 1457.34048
Mohanasubha, R.; Sabiya Shakila, M. I.; Senthilvelan, M.
2
2014
The Prelle-Singer method and Painlevé hierarchies. Zbl 1305.37036
Gordoa, P. R.; Pickering, A.; Senthilvelan, M.
1
2014
Classification of Lie point symmetries for quadratic Liénard type equation \(\ddot{x}+f(x)\dot{x}^2+g(x)=0\). Zbl 1295.34049
Tiwari, Ajey K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
26
2013
On certain new exact solutions of a diffusive predator-prey system. Zbl 1261.35143
Kraenkel, R. A.; Manikandan, K.; Senthilvelan, M.
8
2013
A nonlocal connection between certain linear and nonlinear ordinary differential equations. II: Complex nonlinear oscillators. Zbl 1334.34085
Mohanasubha, R.; Sheeba, Jane H.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
1
2013
Exact quantization of a PT-symmetric (reversible) Liénard-type nonlinear oscillator. Zbl 1252.81055
Ruby, V. Chithiika; Senthilvelan, M.; Lakshmanan, M.
12
2012
On the complete integrability of a nonlinear oscillator from group theoretical perspective. Zbl 1276.81050
Bhuvaneswari, A.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2012
Nonlocal symmetries of Riccati and Abel chains and their similarity reductions. Zbl 1274.34020
Bruzon, M. S.; Gandarias, M. L.; Senthilvelan, M.
7
2012
Multi-loop soliton solutions and their interaction in the Degasperis-Procesi equation. Zbl 1298.37058
Stalin, S.; Senthilvelan, M.
7
2012
Application of the \(\lambda\)-symmetries approach and time independent integral of the modified Emden equation. Zbl 1239.34002
Bhuvaneswari, A.; Kraenkel, Roberto A.; Senthilvelan, Murugaian
5
2012
Ladder operators and squeezed coherent states of a three-dimensional generalized isotonic nonlinear oscillator. Zbl 1275.81052
Ruby, V. Chithiika; Karthiga, S.; Senthilvelan, M.
5
2012
A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator. Zbl 1245.81055
Ruby, V. Chithiika; Senthilvelan, M.
3
2012
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations. I: Scalar case. Zbl 1255.34038
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2012
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations. II: Extension to coupled ODEs. Zbl 1255.34039
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2012
An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator. Zbl 1278.81070
Ruby, V. Chithiika; Senthilvelan, M.
2
2012
On the nonlocal symmetries of certain nonlinear oscillators and their general solution. Zbl 1250.34030
Bruzon, M. S.; Gandarias, M. L.; Senthilvelan, M.
10
2011
A note on the prolongation structure of the cubically nonlinear integrable Camassa-Holm type equation. Zbl 1254.76029
Stalin, S.; Senthilvelan, M.
4
2011
Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order. Zbl 1236.34044
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
3
2011
Lie point symmetries and the time-independent integral of the damped harmonic oscillator. Zbl 1263.70024
Bhuvaneswari, A.; Kraenkel, R. A.; Senthilvelan, M.
2
2011
On the construction of coherent states of position dependent mass Schrödinger equation endowed with effective potential. Zbl 1310.81054
Chithiika Ruby, V.; Senthilvelan, M.
12
2010
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system. Zbl 1309.34007
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2010
A nonlocal connection between certain linear and nonlinear ordinary differential equations: extension to coupled equations. Zbl 1314.34034
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2010
On the generalized intelligent states and certain related nonclassical states of a quantum exactly solvable nonlinear oscillator. Zbl 1200.81084
Ruby, V. Chithiika; Senthilvelan, M.
6
2010
A group theoretical identification of integrable equations in the Liénard-type equation \(\ddot x+f(x)\dot x+g(x) = 0\). II: Equations having maximal Lie point symmetries. Zbl 1283.34036
Pandey, S. N.; Bindu, P. S.; Senthilvelan, M.; Lakshmanan, M.
22
2009
A group theoretical identification of integrable cases of the Liénard-type equation \(\ddot x +f(x)\dot x +g(x)=0\). I: Equations having nonmaximal number of Lie point symmetries. Zbl 1328.34031
Pandey, S. N.; Bindu, P. S.; Senthilvelan, M.; Lakshmanan, M.
14
2009
Nonstandard conserved Hamiltonian structures in dissipative/damped systems: nonlinear generalizations of damped harmonic oscillator. Zbl 1187.34046
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
13
2009
On the solutions of the position-dependent effective mass Schrödinger equation of a nonlinear oscillator related with the isotonic oscillator. Zbl 1179.81057
Kraenkel, R. A.; Senthilvelan, M.
10
2009
Dynamics of a completely integrable \(N\) coupled Liénard-type nonlinear oscillator. Zbl 1182.70025
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
8
2009
On the complete integrability and linearization of nonlinear ordinary differential equations. III. Coupled first-order equations. Zbl 1186.34048
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
7
2009
On the complete integrability and linearization of nonlinear ordinary differential equations. V. Linearization of coupled second-order equations. Zbl 1186.34050
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
6
2009
On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations. Zbl 1186.34049
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
5
2009
Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems. Zbl 1131.34030
Bluman, George; Cheviakov, Alexei F.; Senthilvelan, M.
7
2008
Reply to ‘Comment on “On the general solution for the modified Emden type equation \(\ddot{x}+\alpha x\dot x+\beta x^3=0\)”’. Zbl 1137.34301
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2
2008
On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator. Zbl 1137.70344
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
20
2007
On the general solution for the modified Emden-type equation \(\ddot x+\alpha x\dot x+\beta x^3=0\). Zbl 1128.34003
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
19
2007
A simple and unified approach to identify integrable nonlinear oscillators and systems. Zbl 1111.34003
Chandrasekar, V. K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
44
2006
A unification in the theory of linearization of second-order nonlinear ordinary differential equations. Zbl 1146.34312
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
20
2006
A nonlocal connection between certain linear and nonlinear ordinary differential equations/ oscillators. Zbl 1107.34003
Chandrasekar, V. K.; Senthilvelan, M.; Kundu, Anjan; Lakshmanan, M.
17
2006
On the complete integrability and linearization of nonlinear ordinary differential equations. II: Third-order equations. Zbl 1149.34319
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
16
2006
Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation. Zbl 1089.81019
Senthilvelan, M.; Torrisi, M.; Valenti, A.
8
2006
A note on the Painlevé analysis of a \((2+1)\)-dimensional Camassa-Holm equation. Zbl 1099.35097
Gordoa, P. R.; Pickering, A.; Senthilvelan, M.
2
2006
On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations. Zbl 1186.34046
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
54
2005
Extended Prelle-Singer method and integrability/solvability of a class of nonlinear \(n\)th order ordinary differential equations. Zbl 1362.34002
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
12
2005
Application of extended Prelle–Singer procedure to the generalized modified Emden type equation. Zbl 1086.34500
Chandrasekar, V. K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M.
9
2005
A nonlinear oscillator with quasi-harmonic behaviour: two- and \(n\)-dimensional oscillators. Zbl 1068.37038
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano; Senthilvelan, Murugaian
53
2004
New aspects of integrability of force-free Duffing-van der Pol oscillator and related nonlinear systems. Zbl 1069.34055
Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
22
2004
On the integrability, Bäcklund transformation and symmetry aspects of a generalized Fisher type nonlinear reaction-diffusion equation. Zbl 1061.35037
Bindu, P. S.; Lakshmanan, M.; Senthilvelan, M.
1
2004
On certain new solutions of a simplified model for reacting mixtures. Zbl 1012.76100
Senthilvelan, M.; Torrisi, M.
2
2002
On the extended applications of homogeneous balance method. Zbl 1032.35159
Senthilvelan, M.
52
2001
Symmetry analysis of an integrable reaction-diffusion equation. Zbl 1015.35006
Kraenkel, R. A.; Senthilvelan, M.
6
2001
Singularity structure, symmetries and integrability of generalized Fisher-type nonlinear diffusion equation. Zbl 0992.35077
Bindu, P. S.; Senthilvelan, M.; Lakshmanan, M.
2
2001
Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation. Zbl 1115.37347
Kraenkel, R. A.; Senthilvelan, M.; Zenchuk, A. I.
13
2000
On the integrable perturbations of the Camassa-Holm equation. Zbl 1052.37058
Kraenkel, R. A.; Senthilvelan, M.; Zenchuk, A. I.
7
2000
Potential symmetries and new solutions of a simplified model for reacting mixtures. Zbl 0987.76099
Senthilvelan, M.; Torrisi, M.
4
2000
Lie symmetries, Kac-Moody-Virasoro algebras and integrability of certain \((2+1)\)-dimensional nonlinear evolution equations. Zbl 1119.37324
Senthil Velan, M.; Lakshmanan, M.
16
1998
Invariance analysis of the \((2+1)\)-dimensional long dispersive wave equation. Zbl 0952.35005
Senthil Velan, M.; Lakshmanan, M.
1
1997
Lie symmetries and invariant solutions of the shallow-water equation. Zbl 0864.76018
Velan, M. Senthil; Lakshmanan, M.
8
1996
Lie symmetries, infinite-dimensional Lie algebras and similarity reductions of certain \((2+1)\)-dimensional nonlinear evolution equations. Zbl 1044.37546
Lakshmanan, M.; Senthil Velan, M.
4
1996
Lie symmetries and infinite-dimensional Lie algebras of certain nonlinear dissipative systems. Zbl 0833.34037
Senthil Velan, M.; Lakshmanan, M.
8
1995
Direct integration of generalized Lie or dynamical symmetries of three degrees of freedom nonlinear Hamiltonian systems: Integrability and separability. Zbl 0784.58053
Lakshmanan, M.; Velan, M. Senthil
8
1992
Direct integration of generalized Lie symmetries of nonlinear Hamiltonian systems with two degrees of freedom: Integrability and separability. Zbl 0760.35050
Lakshmanan, M.; Senthil Velan, M.
5
1992
all top 5

Cited by 645 Authors

55 Senthilvelan, Murugaian
38 Lakshmanan, Muthusamy
29 Chandrasekar, V. K.
15 El-Nabulsi, Rami Ahmad
15 Rañada, Manuel F.
12 Cariñena, José F.
11 Özer, Teoman
10 Guha, Partha
10 Sinelshchikov, Dmitry I.
9 Ghose Choudhury, Anindya
9 Kudryashov, Nikolaĭ Alekseevich
8 Bekir, Ahmet
8 Feng, Zhaosheng
8 Pradeep, R. Gladwin
7 Quesne, Christiane
7 Ruby, V. Chithiika
7 Santander, Mariano
6 Bruzón, Maria Santos
6 Gandarias Núñez, Maria Luz
6 Khanra, Barun
6 Mohanasubha, R.
6 Tiwari, Ajey K.
5 Ballesteros, Angel
5 Dai, Zhengde
5 de Lucas, Javier
5 Demina, Maria V.
5 Herranz, Francisco José
5 Leach, Peter Gavin Lawrence
5 Muriel, Concepción
5 Nucci, Maria Clara
5 Paliathanasis, Andronikos
5 Polat, Gülden Gün
5 Saleem, Umair
5 Yusufoğlu (Agadjanov), Elçin
4 Bagchi, Bijan Kumar
4 da Mota, Luis Antonio Campinho Pereira
4 Devi, A. Durga
4 Duarte, L. G. S.
4 Hanif, Y.
4 Mustafa, Omar
4 Qadir, Asghar
4 Schulze-Halberg, Axel
4 Stalin, Seenimuthu
4 Vishnu Priya, N.
4 Yu, Fajun
4 Zedan, Hassan A.
3 Ali, Sajid
3 Bindu, P. S.
3 Blasco, Alfonso
3 Calogero, Francesco A.
3 Chen, Hanlin
3 Chen, Yong
3 Cheviakov, Alexei F.
3 da Costa, Bruno G.
3 Fan, Engui
3 Fring, Andreas
3 Gao, Yitian
3 Gomez, Ignacio S.
3 Gordoa, Pilar Ruiz
3 Gubbiotti, Giorgio
3 Harko, Tiberiu
3 Kim, Hyunsoo
3 Kraenkel, Roberto A.
3 Liu, Jianguo
3 Luo, Shaokai
3 Ma, Wen-Xiu
3 Manikandan, Kannan
3 Romero, Juan Luis
3 Sahadevan, Ramajayam
3 Sarfraz, H.
3 Tian, Bo
3 Xian, Daquan
3 Zhang, Xiaotian
3 Zhang, Yi
3 Zhdanov, Renat Z.
2 Ai, Guo-Ping
2 Ali Akbar, M.
2 Amir, Naila
2 An, Ling
2 Antar, Nalan
2 Avellar, J.
2 Bagarello, Fabio
2 Bentaiba, Mustapha
2 Betchewe, Gambo
2 Bhuvaneswari, A.
2 Bluman, George Wallace
2 Bouetou Bouetou, Thomas
2 Bracken, Paul Francis
2 Campoamor-Stursberg, Rutwig
2 Cao, Qi-Hao
2 Cen, Julia
2 Cevikel, Adem Cengiz
2 Choi, Jin Hyuk
2 Chow, Kwok Wing
2 Dai, Chaoqing
2 Dai, Yun
2 Estévez, Pilar G.
2 Gangopadhyay, Gautam
2 Ghosh, Dibyendu
2 Gutiérrez-Sagredo, Iván
...and 545 more Authors
all top 5

Cited in 110 Serials

70 Journal of Mathematical Physics
31 Chaos, Solitons and Fractals
29 Nonlinear Dynamics
24 Applied Mathematics and Computation
22 Communications in Nonlinear Science and Numerical Simulation
17 Journal of Nonlinear Mathematical Physics
15 Physics Letters. A
15 Journal of Physics A: Mathematical and Theoretical
11 Journal of Mathematical Analysis and Applications
10 Theoretical and Mathematical Physics
10 Applied Mathematics Letters
9 International Journal of Theoretical Physics
9 Chaos
9 Nonlinear Analysis. Real World Applications
8 Wave Motion
7 Physica D
6 Journal of Engineering Mathematics
6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
6 Qualitative Theory of Dynamical Systems
6 Journal of Applied Mathematics
5 Abstract and Applied Analysis
5 International Journal of Nonlinear Sciences and Numerical Simulation
4 International Journal of Modern Physics B
4 Computers & Mathematics with Applications
4 Computer Physics Communications
4 Annals of Physics
4 International Journal of Geometric Methods in Modern Physics
4 Discrete and Continuous Dynamical Systems. Series S
4 Communications in Theoretical Physics
4 Advances in Mathematical Physics
4 Analysis and Mathematical Physics
3 Acta Mechanica
3 Nonlinearity
3 Reports on Mathematical Physics
3 Acta Mathematicae Applicatae Sinica. English Series
3 International Journal of Computer Mathematics
3 Regular and Chaotic Dynamics
3 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences
3 Advances in Difference Equations
3 Chinese Journal of Physics (Taipei)
3 International Journal of Applied and Computational Mathematics
2 Mathematical Methods in the Applied Sciences
2 Physica A
2 Journal of Differential Equations
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Studies in Applied Mathematics
2 Applied Mathematical Modelling
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 Journal of Mathematical Chemistry
2 Mathematical Problems in Engineering
2 International Journal of Differential Equations
2 Quantum Studies: Mathematics and Foundations
2 AIMS Mathematics
1 Modern Physics Letters A
1 Applicable Analysis
1 Classical and Quantum Gravity
1 Communications in Mathematical Physics
1 Computer Methods in Applied Mechanics and Engineering
1 European Journal of Physics
1 Journal of Fluid Mechanics
1 Physics Reports
1 Rocky Mountain Journal of Mathematics
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1 Reviews in Mathematical Physics
1 Journal of Geometry and Physics
1 Acta Mathematica Vietnamica
1 Journal of Computational and Applied Mathematics
1 The Journal of the Indian Mathematical Society. New Series
1 Mathematics and Computers in Simulation
1 Quaestiones Mathematicae
1 Ricerche di Matematica
1 Optimal Control Applications & Methods
1 Numerical Methods for Partial Differential Equations
1 Mathematical and Computer Modelling
1 Journal of Global Optimization
1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
1 Continuum Mechanics and Thermodynamics
1 Tatra Mountains Mathematical Publications
1 Applied Mathematics. Series B (English Edition)
1 Electronic Journal of Differential Equations (EJDE)
1 Computational and Applied Mathematics
1 Journal of the Egyptian Mathematical Society
1 Journal of Lie Theory
1 Complexity
1 Differential Equations and Dynamical Systems
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Journal of Interdisciplinary Mathematics
1 Journal of Dynamical and Control Systems
1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
1 Waves in Random and Complex Media
1 Journal of Biological Dynamics
1 The European Physical Journal B. Condensed Matter and Complex Systems
1 Computational & Mathematical Methods in Medicine
1 Advances in High Energy Physics
1 Asian-European Journal of Mathematics
1 Tbilisi Mathematical Journal
1 Ufimskiĭ Matematicheskiĭ Zhurnal
1 Symmetry
1 Afrika Matematika
...and 10 more Serials
all top 5

Cited in 44 Fields

223 Partial differential equations (35-XX)
159 Ordinary differential equations (34-XX)
130 Dynamical systems and ergodic theory (37-XX)
78 Quantum theory (81-XX)
75 Mechanics of particles and systems (70-XX)
28 Fluid mechanics (76-XX)
20 Numerical analysis (65-XX)
17 Biology and other natural sciences (92-XX)
15 Special functions (33-XX)
13 Computer science (68-XX)
12 Real functions (26-XX)
12 Global analysis, analysis on manifolds (58-XX)
12 Optics, electromagnetic theory (78-XX)
11 Calculus of variations and optimal control; optimization (49-XX)
10 Differential geometry (53-XX)
10 Statistical mechanics, structure of matter (82-XX)
10 Relativity and gravitational theory (83-XX)
7 Nonassociative rings and algebras (17-XX)
6 Topological groups, Lie groups (22-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Mechanics of deformable solids (74-XX)
5 Systems theory; control (93-XX)
4 Operator theory (47-XX)
3 Algebraic geometry (14-XX)
3 Difference and functional equations (39-XX)
3 Geometry (51-XX)
2 Integral transforms, operational calculus (44-XX)
2 Integral equations (45-XX)
2 Probability theory and stochastic processes (60-XX)
2 Statistics (62-XX)
1 General and overarching topics; collections (00-XX)
1 Mathematical logic and foundations (03-XX)
1 General algebraic systems (08-XX)
1 Group theory and generalizations (20-XX)
1 Functions of a complex variable (30-XX)
1 Approximations and expansions (41-XX)
1 Functional analysis (46-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Geophysics (86-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year