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Soliton and Riemann theta function quasi-periodic wave solutions for a \((2+1)\)-dimensional generalized shallow water wave equation

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Abstract

In this paper, a \((2 + 1)\)-dimensional generalized shallow water wave equation is investigated through bilinear Hirota method. Interestingly, the breather-type and lump-type soliton solutions are obtained. Furthermore, dynamic properties of the soliton waves are revealed by means of the asymptotic analysis. Based on Hirota bilinear method and Riemann theta function, we succeed in constructing quasi-periodic wave solutions with a generalized form. We also display the asymptotic properties of these quasi-periodic wave solutions and point out the relation between the quasi-periodic wave solutions and the soliton solutions.

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Acknowledgments

The authors would like to express their sincere thanks to Prof. Liming Ling for his enthusiastic guidance. The work was supported by the National Natural Science foundation of China (Nos. 11171115 and 11361069).

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Yiren Chen & Zhengrong Liu

  2. Department of Mathematics, Shaoxing University, Shaoxing, 312000, People’s Republic of China

    Ming Song

  3. Department of Mathematics, Yuxi Normal University, Yuxi, 653100, People’s Republic of China

    Ming Song

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  1. Yiren Chen
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Correspondence to Zhengrong Liu.

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Chen, Y., Song, M. & Liu, Z. Soliton and Riemann theta function quasi-periodic wave solutions for a \((2+1)\)-dimensional generalized shallow water wave equation. Nonlinear Dyn 82, 333–347 (2015). https://doi.org/10.1007/s11071-015-2161-7

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