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Kapitula, Todd M.

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Author ID: kapitula.todd-m Recent zbMATH articles by "Kapitula, Todd M."
Published as: Kapitula, T.; Kapitula, Todd; Kapitula, Todd M.
Documents Indexed: 49 Publications since 1990, including 2 Books

Publications by Year

Citations contained in zbMATH

46 Publications have been cited 716 times in 434 Documents Cited by Year
Spectral and dynamical stability of nonlinear waves. Zbl 1297.37001
Kapitula, Todd; Promislow, Keith
106
2013
Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations. Zbl 0935.35150
Kapitula, Todd; Sandstede, Björn
53
1998
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Zbl 1056.37080
Kapitula, Todd; Kevrekidis, Panayotis G.; Sandstede, Björn
48
2004
Multidimensional stability of planar travelling waves. Zbl 0866.35021
Kapitula, Todd
45
1997
Stability of travelling waves for non-convex scalar viscous conservation laws. Zbl 0791.35078
Jones, Christopher K. R. T.; Gardner, Robert; Kapitula, Todd
36
1993
On the spectra of periodic waves for infinite-dimensional Hamiltonian systems. Zbl 1155.37039
Hařaǧuş, Mariana; Kapitula, Todd
34
2008
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Zbl 1080.37070
Kapitula, Todd; Kevrekidis, Panayotis G.; Sandstede, Björn
27
2005
On the stability of travelling waves in weighted \(L^ \infty\) spaces. Zbl 0803.35067
Kapitula, Todd
25
1994
An index theorem for the stability of periodic travelling waves of Korteweg-de Vries type. Zbl 1230.35118
Bronski, Jared C.; Johnson, Mathew A.; Kapitula, Todd
23
2011
The orbital stability of the cnoidal waves of the Korteweg-de Vries equation. Zbl 1238.35128
Deconinck, Bernard; Kapitula, Todd
22
2010
Edge bifurcations for near integrable systems via Evans function techniques. Zbl 1092.37048
Kapitula, Todd; Sandstede, Björn
20
2002
On the spectral and orbital stability of spatially periodic stationary solutions of generalized Korteweg-de Vries equations. Zbl 1331.35305
Kapitula, Todd; Deconinck, Bernard
18
2015
On the stability of \(N\)-solitons in integrable systems. Zbl 1138.35085
Kapitula, Todd
16
2007
The Evans function and generalized Melnikov integrals. Zbl 0921.34009
Kapitula, Todd
16
1999
A Hamiltonian-Krein (Instability) index theory for solitary waves to KdV-like eigenvalue problems. Zbl 1288.35422
Kapitula, Todd; Stefanov, Atanas
15
2014
Stability indices for constrained self-adjoint operators. Zbl 1244.35094
Kapitula, Todd; Promislow, Keith
15
2012
Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Zbl 1012.35043
Kapitula, Todd; Rubin, Jonathan
15
2000
The Evans function for nonlocal equations. Zbl 1059.35137
Kapitula, Todd; Kutz, Nathan; Sandstede, Björn
14
2004
Stability of waves in discrete systems. Zbl 1001.37080
Kapitula, Todd; Kevrekidis, Panayotis
13
2001
Nearly real fronts in a Ginzburg-Landau equation. Zbl 0708.76064
Jones, Christopher K. R. T.; Kapitula, Todd M.; Powell, James A.
13
1990
Three is a crowd: solitary waves in photorefractive media with three potential wells. Zbl 1210.35171
Kapitula, Todd; Kevrekidis, P. G.; Chen, Zhigang
12
2006
Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrödinger equation. Zbl 0935.35149
Kapitula, Todd
12
1998
An instability index theory for quadratic pencils and applications. Zbl 1301.35081
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd
10
2014
Eigenvalues and resonances using the Evans function. Zbl 1074.34077
Kapitula, Todd; Sandstede, Björn
10
2004
Stability of waves in perturbed Hamiltonian systems. Zbl 0995.35065
Kapitula, Todd
10
2001
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice. Zbl 1144.37362
Kapitula, Todd; Kevrekidis, P. G.
9
2005
On the nonlinear stability of plane waves for the Ginzburg-Landau equation. Zbl 0808.35054
Kapitula, Todd
9
1994
Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation. Zbl 0895.34042
Kapitula, Todd
8
1996
Linear stability of perturbed Hamiltonian systems: theory and a case example. Zbl 1061.70012
Kapitula, T.; Kevrekidis, P. G.
7
2004
Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation. Zbl 0851.35126
Kapitula, Todd; Maier-Paape, Stanislaus
7
1996
Stability of weak shocks in \(\lambda\) - \(\omega\) systems. Zbl 0756.35050
Kapitula, Todd M.
7
1991
Rotating matter waves in Bose-Einstein condensates. Zbl 1124.35085
Kapitula, Todd; Kevrekidis, P. G.; Carretero-González, R.
6
2007
The Krein signature, Krein eigenvalues, and the Krein oscillation theorem. Zbl 1231.47015
Kapitula, Todd
5
2010
Stability analysis of pulses via the Evans function: dissipative systems. Zbl 1080.35140
Kapitula, T.
5
2005
On the spectral stability of kinks in some \(\mathcal{PT}\)-symmetric variants of the classical Klein-Gordon field theories. Zbl 1304.35608
Demirkaya, A.; Kapitula, T.; Kevrekidis, P. G.; Stanislavova, M.; Stefanov, A.
4
2014
Instability indices for matrix polynomials. Zbl 1283.15060
Kapitula, Todd; Hibma, Elizabeth; Kim, Hwa-Pyeong; Timkovich, Jonathan
3
2013
Interaction of excited states in two-species Bose-Einstein condensates: a case study. Zbl 1183.82005
Kapitula, Todd; Law, Kody J. H.; Kevrekidis, Panayotis G.
3
2010
Exponentially small splitting of heteroclinc orbits: from the rapidly forced pendulum to discrete solitons. Zbl 1115.34328
Kevrekidis, P. G.; Jones, C. K. R. T.; Kapitula, T.
3
2000
Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation. Zbl 0968.35108
Kapitula, Todd
3
1998
Singular heteroclinic orbits for degenerate modulation equations. Zbl 0900.35369
Kapitula, Todd
3
1995
Consensus and clustering in opinion formation on networks. Zbl 1402.91617
Bujalski, Julia; Dwyer, Grace; Kapitula, Todd; Le, Quang-Nhat; Malvai, Harjasleen; Rosenthal-Kay, Jordan; Ruiter, Joshua
1
2018
Existence, stability, and dynamics of harmonically trapped one-dimensional multi-component solitary waves: the near-linear limit. Zbl 1370.35246
Xu, H.; Kevrekidis, P. G.; Kapitula, T.
1
2017
Spots and stripes in nonlinear Schrödinger-type equations with nearly one-dimensional potentials. Zbl 1282.35346
Haragus, Mariana; Kapitula, Todd
1
2014
The Krein matrix: general theory and concrete applications in atomic Bose-Einstein condensates. Zbl 1291.30184
Kapitula, Todd; Kevrekidis, Panayotis G.; Yan, Dong
1
2013
Disk-shaped Bose-Einstein condensates in the presence of an harmonic trap and an optical lattice. Zbl 1307.35280
Kapitula, Todd; Kevrekidis, Panayotis G.; Frantzeskakis, D. J.
1
2008
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation. Zbl 1125.82018
Kapitula, Todd; Kevrekidis, P. G.
1
2005
Consensus and clustering in opinion formation on networks. Zbl 1402.91617
Bujalski, Julia; Dwyer, Grace; Kapitula, Todd; Le, Quang-Nhat; Malvai, Harjasleen; Rosenthal-Kay, Jordan; Ruiter, Joshua
1
2018
Existence, stability, and dynamics of harmonically trapped one-dimensional multi-component solitary waves: the near-linear limit. Zbl 1370.35246
Xu, H.; Kevrekidis, P. G.; Kapitula, T.
1
2017
On the spectral and orbital stability of spatially periodic stationary solutions of generalized Korteweg-de Vries equations. Zbl 1331.35305
Kapitula, Todd; Deconinck, Bernard
18
2015
A Hamiltonian-Krein (Instability) index theory for solitary waves to KdV-like eigenvalue problems. Zbl 1288.35422
Kapitula, Todd; Stefanov, Atanas
15
2014
An instability index theory for quadratic pencils and applications. Zbl 1301.35081
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd
10
2014
On the spectral stability of kinks in some \(\mathcal{PT}\)-symmetric variants of the classical Klein-Gordon field theories. Zbl 1304.35608
Demirkaya, A.; Kapitula, T.; Kevrekidis, P. G.; Stanislavova, M.; Stefanov, A.
4
2014
Spots and stripes in nonlinear Schrödinger-type equations with nearly one-dimensional potentials. Zbl 1282.35346
Haragus, Mariana; Kapitula, Todd
1
2014
Spectral and dynamical stability of nonlinear waves. Zbl 1297.37001
Kapitula, Todd; Promislow, Keith
106
2013
Instability indices for matrix polynomials. Zbl 1283.15060
Kapitula, Todd; Hibma, Elizabeth; Kim, Hwa-Pyeong; Timkovich, Jonathan
3
2013
The Krein matrix: general theory and concrete applications in atomic Bose-Einstein condensates. Zbl 1291.30184
Kapitula, Todd; Kevrekidis, Panayotis G.; Yan, Dong
1
2013
Stability indices for constrained self-adjoint operators. Zbl 1244.35094
Kapitula, Todd; Promislow, Keith
15
2012
An index theorem for the stability of periodic travelling waves of Korteweg-de Vries type. Zbl 1230.35118
Bronski, Jared C.; Johnson, Mathew A.; Kapitula, Todd
23
2011
The orbital stability of the cnoidal waves of the Korteweg-de Vries equation. Zbl 1238.35128
Deconinck, Bernard; Kapitula, Todd
22
2010
The Krein signature, Krein eigenvalues, and the Krein oscillation theorem. Zbl 1231.47015
Kapitula, Todd
5
2010
Interaction of excited states in two-species Bose-Einstein condensates: a case study. Zbl 1183.82005
Kapitula, Todd; Law, Kody J. H.; Kevrekidis, Panayotis G.
3
2010
On the spectra of periodic waves for infinite-dimensional Hamiltonian systems. Zbl 1155.37039
Hařaǧuş, Mariana; Kapitula, Todd
34
2008
Disk-shaped Bose-Einstein condensates in the presence of an harmonic trap and an optical lattice. Zbl 1307.35280
Kapitula, Todd; Kevrekidis, Panayotis G.; Frantzeskakis, D. J.
1
2008
On the stability of \(N\)-solitons in integrable systems. Zbl 1138.35085
Kapitula, Todd
16
2007
Rotating matter waves in Bose-Einstein condensates. Zbl 1124.35085
Kapitula, Todd; Kevrekidis, P. G.; Carretero-González, R.
6
2007
Three is a crowd: solitary waves in photorefractive media with three potential wells. Zbl 1210.35171
Kapitula, Todd; Kevrekidis, P. G.; Chen, Zhigang
12
2006
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Zbl 1080.37070
Kapitula, Todd; Kevrekidis, Panayotis G.; Sandstede, Björn
27
2005
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice. Zbl 1144.37362
Kapitula, Todd; Kevrekidis, P. G.
9
2005
Stability analysis of pulses via the Evans function: dissipative systems. Zbl 1080.35140
Kapitula, T.
5
2005
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation. Zbl 1125.82018
Kapitula, Todd; Kevrekidis, P. G.
1
2005
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Zbl 1056.37080
Kapitula, Todd; Kevrekidis, Panayotis G.; Sandstede, Björn
48
2004
The Evans function for nonlocal equations. Zbl 1059.35137
Kapitula, Todd; Kutz, Nathan; Sandstede, Björn
14
2004
Eigenvalues and resonances using the Evans function. Zbl 1074.34077
Kapitula, Todd; Sandstede, Björn
10
2004
Linear stability of perturbed Hamiltonian systems: theory and a case example. Zbl 1061.70012
Kapitula, T.; Kevrekidis, P. G.
7
2004
Edge bifurcations for near integrable systems via Evans function techniques. Zbl 1092.37048
Kapitula, Todd; Sandstede, Björn
20
2002
Stability of waves in discrete systems. Zbl 1001.37080
Kapitula, Todd; Kevrekidis, Panayotis
13
2001
Stability of waves in perturbed Hamiltonian systems. Zbl 0995.35065
Kapitula, Todd
10
2001
Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Zbl 1012.35043
Kapitula, Todd; Rubin, Jonathan
15
2000
Exponentially small splitting of heteroclinc orbits: from the rapidly forced pendulum to discrete solitons. Zbl 1115.34328
Kevrekidis, P. G.; Jones, C. K. R. T.; Kapitula, T.
3
2000
The Evans function and generalized Melnikov integrals. Zbl 0921.34009
Kapitula, Todd
16
1999
Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations. Zbl 0935.35150
Kapitula, Todd; Sandstede, Björn
53
1998
Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrödinger equation. Zbl 0935.35149
Kapitula, Todd
12
1998
Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation. Zbl 0968.35108
Kapitula, Todd
3
1998
Multidimensional stability of planar travelling waves. Zbl 0866.35021
Kapitula, Todd
45
1997
Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation. Zbl 0895.34042
Kapitula, Todd
8
1996
Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation. Zbl 0851.35126
Kapitula, Todd; Maier-Paape, Stanislaus
7
1996
Singular heteroclinic orbits for degenerate modulation equations. Zbl 0900.35369
Kapitula, Todd
3
1995
On the stability of travelling waves in weighted \(L^ \infty\) spaces. Zbl 0803.35067
Kapitula, Todd
25
1994
On the nonlinear stability of plane waves for the Ginzburg-Landau equation. Zbl 0808.35054
Kapitula, Todd
9
1994
Stability of travelling waves for non-convex scalar viscous conservation laws. Zbl 0791.35078
Jones, Christopher K. R. T.; Gardner, Robert; Kapitula, Todd
36
1993
Stability of weak shocks in \(\lambda\) - \(\omega\) systems. Zbl 0756.35050
Kapitula, Todd M.
7
1991
Nearly real fronts in a Ginzburg-Landau equation. Zbl 0708.76064
Jones, Christopher K. R. T.; Kapitula, Todd M.; Powell, James A.
13
1990
all top 5

Cited by 513 Authors

28 Pelinovsky, Dmitry Efimovich
27 Kevrekidis, Panayotis G.
23 Kapitula, Todd M.
20 Zumbrun, Kevin R.
16 Stefanov, Atanas G.
14 Sandstede, Björn
13 Johnson, Mathew A.
11 Deconinck, Bernard
11 Stanislavova, Milena
10 Howard, Peter
10 Latushkin, Yuri
9 Promislow, Keith Steven
8 Doelman, Arjen
8 Frantzeskakis, Dimitri J.
8 Haragus, Mariana
8 Lafortune, Stéphane
7 Ghazaryan, Anna
7 Hupkes, Hermen Jan
7 Lv, Guangying
7 Marangell, Robert
7 Rodrigues, Luis Miguel
7 Scheel, Arnd
6 Barker, Blake
6 Humpherys, Jeffrey
6 Jones, Christopher K. R. T.
6 Malomed, Boris A.
6 van Heijster, Peter
6 Yang, Jianke
5 Beck, Margaret
5 Bronski, Jared C.
5 de Rijk, Björn
5 Lyng, Gregory Daniel
5 Plaza, Ramón G.
5 Sheng, WeiJie
5 Wang, Zhi Cheng
5 Weinstein, Michael I.
4 Carbou, Gilles
4 Carretero-González, Ricardo
4 Derks, Gianne
4 Gallay, Thierry
4 Goodman, Roy H.
4 Hakkaev, Sevdzhan A.
4 Koch, Othmar
4 Li, Wan-Tong
4 Manukian, Vahagn
4 Noble, Pascal
4 Paleari, Simone
4 Pastor, Ademir
4 Penati, Tiziano
4 Pogan, Alin
4 Sukhtayev, Alim
4 Trichtchenko, Olga
4 Wang, Mingxin
4 Weinmüller, Ewa B.
4 Wu, Qiliang
3 Alejo, Miguel A.
3 Angulo Pava, Jaime
3 Benzoni-Gavage, Sylvie
3 Beyn, Wolf-Jürgen
3 Bishop, Alan Reginald
3 Borisov, Denis Ivanovich
3 Bridges, Thomas J.
3 Comech, Andrew
3 Cox, Graham
3 Demirkaya, Aslihan
3 Erbay, Husnuata A.
3 Erbay, Saadet
3 Erkip, Albert Kohen
3 Faye, Grégory
3 Feng, Wen
3 Geyer, Anna
3 Hamster, C. H. S.
3 Hoffman, Aaron
3 Holzer, Matt
3 Hur, Vera Mikyoung
3 Il’ichev, Andreĭ Teĭmurazovich
3 Malham, Simon J. A.
3 Marzuola, Jeremy L.
3 Mizumachi, Tetsu
3 Muñoz, Claudio
3 Natali, Fábio M. Amorin
3 Panayotaros, Panayotis
3 Rademacher, Jens Diederich Michael
3 Sansottera, Marco
3 Schneider, Guido
3 Van Vleck, Erik S.
3 Wang, Xiaohuan
3 Wayne, C. Eugene
2 Auzinger, Winfried
2 Binder, Benjamin James
2 Boussaid, Nabile
2 Carter, John D.
2 Carter, Paul M.
2 Champneys, Alan R.
2 Chang, Shing-Lin
2 Chen, Chaonien
2 Chen, Huei-Shuang
2 Chen, Jinbing
2 Chien, Cheng-Sheng
2 Chugunova, Marina A.
...and 413 more Authors
all top 5

Cited in 101 Serials

71 Physica D
46 Journal of Differential Equations
15 SIAM Journal on Mathematical Analysis
13 Archive for Rational Mechanics and Analysis
12 Journal of Mathematical Analysis and Applications
12 Studies in Applied Mathematics
11 Communications in Mathematical Physics
11 Journal of Mathematical Physics
10 Journal of Nonlinear Science
9 Physics Letters. A
9 Discrete and Continuous Dynamical Systems
8 SIAM Journal on Applied Dynamical Systems
7 Nonlinearity
7 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
6 ZAMP. Zeitschrift für angewandte Mathematik und Physik
6 SIAM Journal on Applied Mathematics
6 Journal of Dynamics and Differential Equations
5 Mathematics of Computation
5 Transactions of the American Mathematical Society
5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
5 Chaos
5 Communications in Nonlinear Science and Numerical Simulation
4 Journal of Computational and Applied Mathematics
4 Journal of Functional Analysis
4 Proceedings of the American Mathematical Society
4 Communications in Partial Differential Equations
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 Science China. Mathematics
3 Journal of Fluid Mechanics
3 Journal of Mathematical Biology
3 Mathematical Methods in the Applied Sciences
3 Chaos, Solitons and Fractals
3 Applied Mathematics and Computation
3 Mathematics and Computers in Simulation
3 Applied Mathematics Letters
3 Linear Algebra and its Applications
3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
3 Nonlinear Analysis. Real World Applications
3 Discrete and Continuous Dynamical Systems. Series B
3 Communications on Pure and Applied Analysis
3 Journal of Hyperbolic Differential Equations
2 Applicable Analysis
2 Biological Cybernetics
2 Letters in Mathematical Physics
2 Theoretical and Mathematical Physics
2 Integral Equations and Operator Theory
2 Memoirs of the American Mathematical Society
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Quarterly of Applied Mathematics
2 SIAM Journal on Numerical Analysis
2 Zeitschrift für Analysis und ihre Anwendungen
2 Applied Numerical Mathematics
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
2 Journal of Nonlinear Mathematical Physics
2 Dynamical Systems
2 Physical Review E. Third Series
2 Journal of Physics A: Mathematical and Theoretical
2 Nonlinear Analysis. Theory, Methods & Applications
2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Computers & Mathematics with Applications
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Mathematical Biosciences
1 Physics Reports
1 Reviews of Modern Physics
1 Advances in Mathematics
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 BIT
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1 Inventiones Mathematicae
1 Kybernetika
1 Le Matematiche
1 Mathematische Nachrichten
1 Monatshefte für Mathematik
1 Numerische Mathematik
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Journal of the American Mathematical Society
1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1 Numerical Algorithms
1 Calculus of Variations and Partial Differential Equations
1 Journal of Mathematical Sciences (New York)
1 Kyushu Journal of Mathematics
1 Mathematical Problems in Engineering
1 Mathematics and Mechanics of Solids
1 Nonlinear Dynamics
1 Abstract and Applied Analysis
1 Taiwanese Journal of Mathematics
1 Wuhan University Journal of Natural Sciences (WUJNS)
1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Acta Mathematica Sinica. English Series
1 Advanced Nonlinear Studies
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Milan Journal of Mathematics
1 Proceedings of the Steklov Institute of Mathematics
1 Nonlinear Oscillations
1 Mathematical Modelling of Natural Phenomena
1 Discrete and Continuous Dynamical Systems. Series S
1 São Paulo Journal of Mathematical Sciences
1 Advances in Mathematical Physics
1 Journal of Theoretical Biology
...and 1 more Serials

Citations by Year