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Spatiotemporal deformation of multi-soliton to (2 + 1)-dimensional KdV equation

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Abstract

This work proposes a three-wave method with a perturbation parameter to obtain exact multi-soliton solutions of nonlinear evolution equation. The (\(2+1\))-dimensional KdV equation is used as an example to illustrate the effectiveness of the suggested method. Using this method, new multi-soliton solutions are given. Specially, spatiotemporal dynamics of breather two-soliton and multi-soliton including deformation between bright and dark multi-soliton each other, and deflection with different directions and angles are investigated and exhibited to (\(2+1\))D KdV equation. Some new nonlinear phenomena are revealed under the small perturbation of parameter.

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Acknowledgments

The work was supported in part by the State Administration of Foreign Experts Affairs of China, the National Natural Science Foundation of China (No. 10801037, No.11361048), the New Teacher Grant of Ministry of Education of China (No.20080246), the Young Teachers Foundation (No. 1411018) of Fudan university and Qujin Normal University NSF Grant ( No.2010QN018).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Qujing Normal University, Qujing, 655011, People’s Republic of China

    Jun Liu, Gui Mu & Hongying Luo

  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, People’s Republic of China

    Zhengde Dai

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  1. Jun Liu
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  2. Gui Mu
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  3. Zhengde Dai
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  4. Hongying Luo
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Correspondence to Zhengde Dai.

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Liu, J., Mu, G., Dai, Z. et al. Spatiotemporal deformation of multi-soliton to (2 + 1)-dimensional KdV equation. Nonlinear Dyn 83, 355–360 (2016). https://doi.org/10.1007/s11071-015-2332-6

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