Exact travelling wave solutions and their dynamicalbehavior for a class coupled nonlinear wave equations

Jibin Li; Fengjuan Chen

doi:10.3934/dcdsb.2013.18.163

Article Contents

2013, Volume 18, Issue 1: 163-172. Doi: 10.3934/dcdsb.2013.18.163

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Exact travelling wave solutions and their dynamical behavior for a class coupled nonlinear wave equations

Jibin Li^1, and
Fengjuan Chen^1,

1.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004

Received: March 2012

Revised: July 2012

Published: January 2013

Abstract / Introduction Related Papers Cited by

Abstract

For the system of KP like equation coupled to a Schrödinger equation, a corresponding four-dimensional travelling wave systems and a two-order linear non-autonomous system are studied by using Congrove's results and dynamical system method. For the four-dimensional travelling wave systems, exact explicit homoclinic orbit families, periodic and quasi-periodic wave solution families are obtained. The existence of homoclinic manifolds to four kinds of equilibria including a hyperbolic equilibrium, a center-saddle and an equilibrium with zero pair of eigenvalues is revealed. For the two-order linear non-autonomous system, the dynamical behavior of the bounded solutions is discussed.

Keywords:

Mathematics Subject Classification: 34A26, 34C15, 34C23, 34C37, 35C07, 35C08, 37J35, 37K40.

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References

[1]	X. B. Hu, The higher order KdV equation with a source and nonlinear superposition formula, Chaos, Solitonsand Fract., 7 (1996), 211-215.
[2]	S. Z. Rida and M. Khalfallah, New periodic wave and soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation, Commun. nonlinear Sci. Numer. Simulat., 15 (2010), 2818-2827.
[3]	M. C. Cosgrove, Higher-order Painleve equations in the polynomial class I. Bureau symbol P2, Stud. Appl. Math., 104 (2000), 1-65.
[4]	A. M. Wazwaz, Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method, Appl. Math. Comput., 182 (2006), 283-300.
[5]	A. M. Wazwaz, The integrable KdV6 equations: multiple solitons and multiple singular soliton solutions, Appl. Math. Comput., 204 (2008), 963-972.
[6]	J. K. Hale, "Ordinary Differential Equation," second Edition, Robert E.Krieger Publishing Company: Huntington, New York, 1980.
[7]	L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Springer-Verlag, Berlinm, (1959), vii+271 pp.