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Deformation rogue wave to the (2+1)-dimensional KdV equation

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Abstract

Deformation rogue wave as exact solution of the (2+1)-dimensional Korteweg–de Vries (KdV) equation is obtained via the bilinear method. It is localized in both time and space and is derived by the interaction between lump soliton and a pair of resonance stripe solitons. In contrast to the general method to get the rogue wave, we mainly combine the positive quadratic function and the hyperbolic cosine function, and then the lump soliton can be evolved rogue wave. Under the small perturbation of parameter, rich dynamic phenomena are depicted both theoretically and graphically so as to understand the property of (2+1)-dimensional KdV equation deeply. In general terms, these deformations mainly have three types: two rogue waves, one rogue wave or no rogue wave.

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Acknowledgements

We would like to express our sincere thanks to S. Y. Lou, W. X. Ma, E. G. Fan, Z. Y. Yan, X. Y. Tang, J. C. Chen, X. Wang and other members of our discussion group for their valuable comments.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Xiaoen Zhang & Yong Chen

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  1. Xiaoen Zhang
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  2. Yong Chen
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Correspondence to Yong Chen.

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The project is supported by the Global Change Research Program of China (No. 2015CB953904), National Natural Science Foundation of China (Nos. 11275072, 11435005, 11675054) and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (No. ZF1213).

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Zhang, X., Chen, Y. Deformation rogue wave to the (2+1)-dimensional KdV equation. Nonlinear Dyn 90, 755–763 (2017). https://doi.org/10.1007/s11071-017-3757-x

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  • DOI: https://doi.org/10.1007/s11071-017-3757-x

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