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General \({\varvec{M}}\)-lump, high-order breather and localized interaction solutions to the \(\varvec{2+1}\)-dimensional Sawada–Kotera equation

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Abstract

The \(2+1\)-dimensional Sawada–Kotera equation is an important physical model. Here, by taking a long limit and restricting a conjugation condition to the related solitons, the general M-lump, high-order breather and localized interaction hybrid solutions are constructed, correspondingly. In order to study the dynamical behaviors, numerical simulations are implemented, which show that the parameters selected have great impacts on the types, dynamical behaviors and propagation properties of the solutions. The method proposed can be effectively applied to construct M-lumps, high-order breathers and interaction solutions of many nonlinear equations. The results obtained can be used to study the propagation phenomena of other nonlinear localized waves.

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Acknowledgements

The authors would like to express their sincere thanks to the reviewers for the kind comments and valuable suggestions. This work is supported by the National Natural Science Foundation of China under Grant No. 11775116, Scientific Foundation for Advanced Talents of Nanjing Forestry University undr Grant No. GXL011 and Jiangsu Provincial Natural Science Foundation under Grant No. BK20150984.

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Authors and Affiliations

  1. College of Sciences, Nanjing Agricultural University, Nanjing, 210095, People’s Republic of China

    Hongli An & Dali Feng

  2. College of Economics and Management, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Haixing Zhu

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  1. Hongli An
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Correspondence to Hongli An.

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An, H., Feng, D. & Zhu, H. General \({\varvec{M}}\)-lump, high-order breather and localized interaction solutions to the \(\varvec{2+1}\)-dimensional Sawada–Kotera equation. Nonlinear Dyn 98, 1275–1286 (2019). https://doi.org/10.1007/s11071-019-05261-6

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