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Spatiotemporal deformation of lump solution to (2+1)-dimensional KdV equation

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Abstract

In this paper, we extend the recent work of Liu and his collaborators for the (2+1)-dimensional KdV equation. The lump solution under the small perturbation of parameter which decays to the background plane wave in all directions in the plane is obtained. This solution is analogous to the lump solution of the KP equation, but there are some novel different features. The deformation between and among bright, bright-dark and dark lump solution is investigated and exhibited mathematically and graphically. We also discuss that the deflection of lump solution not only depends on the perturbation parameter \(u_0\), but also has a relationship with the other parameters. These interesting nonlinear phenomena might provide us with useful information on the dynamics of the relevant fields in nonlinear science.

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Acknowledgments

The author would like to express his sincere thanks to referees for their enthusiastic guidance and help. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11301235, 11261049, 11161025,11501266) and the Fund for Fostering Talents in Kunming University of Science and Technology (Nos: KKSY201403049, KKSY201307141 ).

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  1. School of Science, Kunming University of Science and Technology, Kunming, 650093, China

    Chuanjian Wang

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  1. Chuanjian Wang
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Correspondence to Chuanjian Wang.

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Wang, C. Spatiotemporal deformation of lump solution to (2+1)-dimensional KdV equation. Nonlinear Dyn 84, 697–702 (2016). https://doi.org/10.1007/s11071-015-2519-x

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  • DOI: https://doi.org/10.1007/s11071-015-2519-x

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