Bifurcations and new exact travelling wave solutions for the bidirectional wave equations

Pramana

SHUHUA ZHENG¹  HENG WANG1²  XIAOCHUN HONG³  LONGWEI CHEN³ 

[1] Investment and Development Department, Market and Investment Center, Yunnan Water Investment Co., Limited (06839.HK), Kunming, 650106, People’s Republic of China$$;College of Global Change and Earth System Science, Beijing Normal University, Beijing, 100875, People’s Republic of China$$;College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, People’s Republic of China$$

关键词: Bidirectional wave equations;    dynamical system method;    phase portrait;    dark soliton solution;    bright soliton solution;    periodic travelling wave solution.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of {it Maple} software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional waveequations. The results presented in this paper improve the related previous studies.

【 授权许可】

Unknown