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The Riemann–Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient (\(\varvec{2+1}\))-dimensional KdV equation

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Abstract

In this paper, the Riemann–Bäcklund method is extended to a generalized variable coefficient (\(2+1\))-dimensional Korteweg–de Vries equation. The soliton and quasiperiodic wave solutions are investigated systematically. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. It is proved that the periodic wave solutions tend to the soliton solutions under a small amplitude limit. Furthermore, the propagation characteristics of the soliton solutions and periodic wave solutions are discussed through the graphical analysis.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 41474102. The first author thanks Dr. Yang Li and Dr. Qinglong He of HIT for their helpful discussions.

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  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Zhonglong Zhao & Bo Han

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  1. Zhonglong Zhao
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  2. Bo Han
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Correspondence to Zhonglong Zhao.

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Zhao, Z., Han, B. The Riemann–Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient (\(\varvec{2+1}\))-dimensional KdV equation. Nonlinear Dyn 87, 2661–2676 (2017). https://doi.org/10.1007/s11071-016-3219-x

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