The extended hyperbolic function method and exact solutions of the long-short wave resonance equations
The extended hyperbolic function method and exact solutions of the long-short wave resonance equations
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长短波共振方程的扩展双曲函数法及精确解
DOI：
10.1016/j.chaos.2006.07.007
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发表时间：
2008-05-01
影响因子：
7.8
通讯作者：
Shang, Yadong
中科院分区：
文献类型：
--
作者：
Shang, Yadong
提出了求解非线性波动方程的扩展双曲函数方法。基于这种方法，我们得到了描述长短波共振相互作用的非线性演化方程的多重精确显式解。本文得到的解包括：（a）S和L的钟型孤波解，（B）S的扭型孤波解和L的钟型孤波解，（c）S和L的钟型和扭型复合孤波解，（d）奇异行波解，（e）三角函数型周期行波解，和有理函数型的孤波解。说明了长短波方程精确解的结构变化。本文提出的方法也可用于求解n维非线性波动方程的精确解。(c)2006爱思唯尔有限公司保留所有权利。
The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions. (c) 2006 Elsevier Ltd. All rights reserved.