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Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation. (English) Zbl 1334.76096

Summary: This paper obtains soliton and other solutions to the Gardner-Kadomtsev-Petviashvili equation that models shallow water wave equation in \((1+2)\)-dimensions. There are three types of integration architectures that will be employed in order to obtain several forms of solution to this model. These are traveling wave hypothesis, improved \(G^{'}/G\)-expansion method and finally the tanh-coth hypothesis. The constraint conditions that are needed, for these solutions to exist, are also reported.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35C05 Solutions to PDEs in closed form
35Q35 PDEs in connection with fluid mechanics
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[1] M. Antonova, Adiabatic parameter dynamics of perturbed solitons,, Communications in Nonlinear Science and Numerical Simulation, 14, 734 (2009) · Zbl 1221.35321 · doi:10.1016/j.cnsns.2007.12.004
[2] A. H. Bhrawy, Solitons and other solutions to Kadomtsev-Petviashvili equation of B-type,, Romanian Journal of Physics, 58, 729 (2013)
[3] A. Biswas, Soliton perturbation theory for the Gardner equation,, Advanced Studies in Theoretical Physics, 2, 787 (2008) · Zbl 1157.35466
[4] A. Biswas, 1-soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity,, Applied Mathematics and Computation, 214, 645 (2009) · Zbl 1172.35476 · doi:10.1016/j.amc.2009.04.001
[5] A. Biswas, Topological 1-soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity,, Applied Mathematics and Computation, 217, 1771 (2010) · Zbl 1202.35215 · doi:10.1016/j.amc.2009.09.042
[6] R. Choudhury, Viscelastic MHD free convective flow through porous media in presence of radiation and chemical reaction with heat and mass transfer,, Journal of Applied Fluid Mechanics, 7, 603 (2014)
[7] G. Ebadi, Solitons and other solutions to (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity,, Romaninan Reports in Physics, 65, 27 (2013)
[8] M. Eslami, Soliton solutions of the resonant nonlinear Schrodinger’s equation in optical fibers with time-dependent coefficients by simplest equation approach,, Journal of Modern Optics, 60, 1627 (2013) · doi:10.1080/09500340.2013.850777
[9] M. Eslami, Topological 1-soliton solution of nonlinear Schrodinger equation with dual-power law nonlinearity in nonlinear optical fibers,, European Physical Journal, 128 (2013)
[10] E. V. Krishnan, A study of shallow water waves with Gardner’s equation,, Nonlinear Dynamics, 66, 497 (2011) · Zbl 1356.76045 · doi:10.1007/s11071-010-9928-7
[11] S. Kundu, An explicit model for concentration distribution using biquadratic log-wake law in an open channel flow,, Journal of Applied Fluid Mechanics, 6, 339 (2013)
[12] Z. G. Makukula, Spectral homotopy analysis method for PDEs that model the unsteady Von Karma swirling flow,, Journal of Applied Fluid Mechanics, 7, 711 (2014)
[13] M. Mirzazadeh, Soliton solutions of the generalized Klein-Gordon equation by using \({G'}/G\)-expansion method,, Computational and Applied Mathematics, 33, 831 (2014) · Zbl 1307.35249 · doi:10.1007/s40314-013-0098-3
[14] M. Mirzazadeh, Exact solutions for nonlinear variants of Kadomtsev-Petviashvili (n, n) equation using functional variable method,, Pramana, 81, 225 (2013)
[15] A. Nazarzadeh, Exact solutions of some nonlinear partial differential equations using functional variable method,, Pramana, 81, 225 (2013) · doi:10.1007/s12043-013-0565-9
[16] D. Pal, Effects of radiation on Darcey-Forchheimer convective flow over a stretching sheet in a micropolar fluid with a non-uniform heat source/sink,, Journal of Applied Fluid Mechanics, 8, 207 (2015)
[17] P. Ram, Rotationally symmetric ferrofluid flow and heat transfer in porous medium with variable viscosity and viscous dissipation,, Journal of Applied Fluid Mechanics, 7, 357 (2014)
[18] S. M. Shafiof, New solutions for positive and negative Gardner-KP equations,, World Applied Science Journal, 13, 662 (2011)
[19] N. Taghizadeh, The simplest equation method to study perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity,, Communications in Nonlinear Science and Numerical Simulations, 17, 1493 (2012) · Zbl 1245.35121 · doi:10.1016/j.cnsns.2011.09.023
[20] N. Taghizadeh, Exact soliton solutions of the modified KdV-KP equation and the Burgers-KP equation by using the first integral method,, Applied Mathematical Modelling, 35, 3991 (2011) · Zbl 1221.35366 · doi:10.1016/j.apm.2011.02.001
[21] N. Taghizadeh, Exact solutions of some nonlinear evolution equations via the first integral method,, Ain Shams Engineering Journal, 4, 493 (2013) · doi:10.1016/j.asej.2012.10.002
[22] W. M. Taha, New exact solutions of sixth-order thin-film equation,, Journal of King Saud University- Science, 26, 75 (2014) · doi:10.1016/j.jksus.2013.07.001
[23] F. Tascan, Travelling wave solutions of nonlinear evolutions by using the first integral method,, Communications in Nonlinear Science and Numerical Simulations, 14, 1810 (2009) · Zbl 1162.35304 · doi:10.1016/j.cnsns.2008.07.009
[24] F. Tascan, Travelling wave solutions of the Cahn-Allen equation by using first integral method,, Applied Mathematics and Computation, 207, 279 (2009) · Zbl 1162.35304 · doi:10.1016/j.amc.2008.10.031
[25] H. Triki, Shock wave solutions of the variants of Kadomtsev-Petviashvili equation,, Canadian Journal of Physics, 89, 979 (2011) · doi:10.1139/p11-083
[26] M. L. Wang, The \({G'}/G\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,, Physics Letters A, 372, 417 (2008) · Zbl 1217.76023 · doi:10.1016/j.physleta.2007.07.051
[27] A. M. Wazwaz, Solitons and singular solutions for the Gardner-KP equation,, Applied Mathematics and Computation, 204, 162 (2008) · Zbl 1159.35432 · doi:10.1016/j.amc.2008.06.011
[28] A. Yildirim, New exact travelling wave solutions for DS-I and DS-II equations,, Nonlinear Analysis: Modelling and Control, 17, 369 (2012) · Zbl 1308.35052
[29] E. Zayed, Some applications of the \({G'}/G\)-expansion method to non-linear partial differential equations,, Applied Mathematics and Computation, 212, 1 (2009) · Zbl 1166.65386 · doi:10.1016/j.amc.2009.02.009
[30] J. Zhang, An improved \({G'}/G\)-expansion method for solving nonlinear evolution equations,, International Journal of Computer Mathematics, 87, 1716 (2010) · Zbl 1197.65161 · doi:10.1080/00207160802450166
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