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Riemann theta solutions and their asymptotic property for a (3\(+\)1)-dimensional water wave equation

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Abstract

In this paper, we consider the (3\(+\)1)-dimensional water wave equation \(u_{yzt}+u_{xxxyz}-6u_{x}u_{xyz}-6u_{xy}u_{xz}=0.\) Based on Bell polynomials, we obtain its Hirota bilinear equation which enable us to acquire Riemann theta solutions including arbitrary differentiable functions. Furthermore, we analyze the asymptotic property of these solutions and reveal the relationship between these 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 (No. 11571116)

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

    Yiren Chen & Zhengrong Liu

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  1. Yiren Chen
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Chen, Y., Liu, Z. Riemann theta solutions and their asymptotic property for a (3\(+\)1)-dimensional water wave equation. Nonlinear Dyn 87, 1069–1080 (2017). https://doi.org/10.1007/s11071-016-3098-1

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