Exact solutions and multi-symplectic structure of the generalized KdV-type equation

Advances in Difference Equations

Xiao-Feng Yang¹  Qing-Jun Li²  Zi-Chen Deng³  Yi Wei³ 

[1] Department of Applied Mathematics, Northwestern Polytechnical University, Xi’School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, P.R. China

关键词: homogeneous balance of undetermined coefficients method;    multi-symplectic structure;    generalized KdV-type equation;    bilinear equation;    N-soliton solution;    traveling wave solution;    35Q55;    35Q80;    35G25;   

DOI  :  10.1186/s13662-015-0611-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The homogeneous balance of undetermined coefficients method is proposed to obtain not only exact solutions but also multi-symplectic structure of some nonlinear partial differential equations. Bilinear equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained by applying the proposed method to the KdV equation. Accordingly, the definition and multi-symplectic structure of the generalized KdV-type equation are given. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear partial differential equations.

【 授权许可】

CC BY