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Zbl 1159.65351
Zhang, Li-Hua
Travelling wave solutions for the generalized Zakharov-Kuznetsov equation with higher-order nonlinear terms. (English)
[J] Appl. Math. Comput. 208, No. 1, 144-155 (2009). ISSN 0096-3003

Summary: With the aid of symbolic computation and two auxiliary ordinary differential equations, the new generalized algebraic method is extended to the generalized Zakharov-Kuznetsov (GZK) equation with higher-order nonlinear terms for constructing a series of new and more general travelling wave solutions. Because of the higher-order nonlinear terms, the equation can not be directly dealt with by the method and require some kinds of techniques. By means of two proper transformations, we transform the GZK equation to an ordinary differential equation that is easy to solve and find a rich variety of new exact travelling wave solutions for the GZK equation, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, combined Jacobi elliptic function solutions and rational function solutions. The method used here can be also extended to other nonlinear partial differential equations with higher-order nonlinear terms.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35Q51 Solitons
35Q53 KdV-like equations

Keywords: generalized Zakharov-Kuznetsov equation; travelling wave solutions; soliton solutions; symbolic computation; higher-order nonlinear terms; periodic solutions; Jacobi elliptic function solutions; rational function solutions

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