The auxiliary elliptic-like equation and the exp-function method

Pramana

Hong Li¹  Jin-Liang Zhang2² 

[1] College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, China$$;College of Science, Henan University of Science and Technology, Luoyang, 471003, China$$

关键词: Auxiliary equation method;    exp-function method;    exact solution;    RKL models;    high-order nonlinear Schrödinger equation;    Hamilton amplitude equation;    generalized Hirota–Satsuma coupled KdV system;    generalized ZK–BBM equation.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The auxiliary equation method is very useful for finding the exact solutions of the nonlinear evolution equations. In this paper, a new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary elliptic-like equation are derived using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. As examples, the RKL models, the high-order nonlinear Schrödinger equation, the Hamilton amplitude equation, the generalized Hirota–Satsuma coupled KdV system and the generalized ZK–BBM equation are investigated and the exact solutions are presented using this method.

【 授权许可】

Unknown