Travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov () system

✍ Scribed by Xijun Deng; Jinlong Cao; Xi Li

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 240 KB
• Volume: 15
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2009.03.023

✦ Synopsis

a b s t r a c t

In this paper, travelling wave solutions for the nonlinear dispersion Drinfel'd-Sokolov system (called Dðm; nÞ system) are studied by using the Weierstrass elliptic function method. As a result, more new exact travelling wave solutions to the Dðm; nÞ system are obtained including not only all the known solutions found by Xie and Yan but also other more general solutions for different parameters m; n. Moreover, it is also shown that the Dðm; 1Þ system with linear dispersion possess compacton and solitary pattern solutions. Besides that, it should be pointed out that the approach is direct and easily carried out without the aid of mathematical software if compared with other traditional methods. We believe that the method can be widely applied to other similar types of nonlinear partial differential equations (PDEs) or systems in mathematical physics.