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

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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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Acknowledgements

The authors gratefully acknowledge the support of the National Science Foundation of China under Grant No. 11261049 and the National Science Foundation of China under Grant No. 11161038.

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Authors and Affiliations

  1. College of Global Change and Earth System Science, Beijing Normal University, Beijing, 100875, People’s Republic of China

    HENG WANG

  2. Investment and Development Department, Market and Investment Center, Yunnan Water Investment Co., Limited (06839.HK), Kunming, 650106, People’s Republic of China

    SHUHUA ZHENG

  3. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, People’s Republic of China

    LONGWEI CHEN & XIAOCHUN HONG

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  1. HENG WANG
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  2. SHUHUA ZHENG
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  3. LONGWEI CHEN
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  4. XIAOCHUN HONG
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WANG, H., ZHENG, S., CHEN, L. et al. Bifurcations and new exact travelling wave solutions for the bidirectional wave equations. Pramana - J Phys 87, 77 (2016). https://doi.org/10.1007/s12043-016-1274-y

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  • DOI: https://doi.org/10.1007/s12043-016-1274-y

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