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Lump solutions to the (\(\mathbf 2+1 \))-dimensional Sawada–Kotera equation

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Abstract

In this paper, via generalized bilinear forms, we consider the (\(2+1\))-dimensional bilinear p-Sawada–Kotera (SK) equation. We derive analytical rational solutions in terms of positive quadratic functions. Through applying the dependent transformation, we present a class of lump solutions of the (\(2+1\))-dimensional SK equation. Those rationally decaying solutions in all space directions exhibit two kinds of characters, i.e., bright lump wave (one peak and two valleys) and bright–dark lump wave (one peak and one valley). In addition, we also obtain three families of bright–dark lump wave solutions to the nonlinear p-SK equation for \(p=3\).

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Acknowledgements

This work was supported by the Shanghai Leading Academic Discipline Project under Grant No. XTKX2012, by the Technology Research and Development Program of University of Shanghai for Science and Technology, by Hujiang Foundation of China under Grant No. B14005 and by the National Natural Science Foundation of China under Grant No. 11201302. The second author was supported in part by the National Natural Science Foundation of China under Grant Nos. 11371326, 11371323, 11271008 and 11371086, Natural Science Foundation of Shanghai under Grant No. 11ZR1414100, Zhejiang Innovation Project of China under Grant No. T200905, the First-class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project (No. A13-0101-12-004) and the Distinguished Professorships of Shanghai University of Electric Power and Shanghai Second Polytechnic University.

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Correspondence to Hai-Qiang Zhang.

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Zhang, HQ., Ma, WX. Lump solutions to the (\(\mathbf 2+1 \))-dimensional Sawada–Kotera equation. Nonlinear Dyn 87, 2305–2310 (2017). https://doi.org/10.1007/s11071-016-3190-6

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  • DOI: https://doi.org/10.1007/s11071-016-3190-6

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