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

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January 2013, 18(1): 163-172. doi: 10.3934/dcdsb.2013.18.163

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

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

Received March 2012 Revised July 2012 Published September 2012

Abstract
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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: quasi-periodic wave solution, homoclinic manifold, center manifold, integrable system., Exact solution.

Mathematics Subject Classification: 34A26, 34C15, 34C23, 34C37, 35C07, 35C08, 37J35, 37K4.

Citation: Jibin Li, Fengjuan Chen. Exact travelling wave solutions and their dynamical behavior for a class coupled nonlinear wave equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 163-172. doi: 10.3934/dcdsb.2013.18.163

References:

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show all references

References:

[1]	X. B. Hu, The higher order KdV equation with a source and nonlinear superposition formula,, Chaos, 7 (1996), 211.
[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.
[3]	M. C. Cosgrove, Higher-order Painleve equations in the polynomial class I. Bureau symbol P2,, Stud. Appl. Math., 104 (2000), 1.
[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.
[5]	A. M. Wazwaz, The integrable KdV6 equations: multiple solitons and multiple singular soliton solutions,, Appl. Math. Comput., 204 (2008), 963.
[6]	J. K. Hale, "Ordinary Differential Equation,", second Edition, (1980).
[7]	L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations,, Springer-Verlag, (1959).

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