Bifurcations and new exact travelling wave solutions for the bidirectional wave equations |
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| Authors: | HENG WANG SHUHUA ZHENG LONGWEI CHEN XIAOCHUN HONG |
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| Affiliation: | 1.College of Global Change and Earth System Science,Beijing Normal University,Beijing,People’s Republic of China;2.Investment and Development Department, Market and Investment Center,Yunnan Water Investment Co., Limited (06839.HK),Kunming,People’s Republic of China;3.College of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming,People’s Republic of China |
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| Abstract: | 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 Maple software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional wave equations. The results presented in this paper improve the related previous studies. |
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