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Interactional solutions of a lump and a solitary wave for two higher-dimensional equations

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Abstract

In this paper, by using the bilinear equation and different test functions, we obtain lump–bell solutions for the \((4+1)\)-dimensional Fokas equation, which describe nonelastic and elastic interactions. We consider various interactions of the lump–bell solutions including fusion, fission, catch-up and head-on. The asymptotic behaviors and dynamics of lump–bell solutions are analyzed graphically. With a scaling transformation, we also obtain the lump–kink solution which describes elastic interactions of a lump- and a kink-type wave for the \((3+1)\)-dimensional potential Yu–Toda–Sasa–Fukuyama equation.

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Acknowledgements

The work described in this paper was supported by National Natural Science Foundation of China (11471215).

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  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Hong-Qian Sun & Ai-Hua Chen

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  1. Hong-Qian Sun
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Author Ai-Hua Chen is one of the members of the above-mentioned project.

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Sun, HQ., Chen, AH. Interactional solutions of a lump and a solitary wave for two higher-dimensional equations. Nonlinear Dyn 94, 1753–1762 (2018). https://doi.org/10.1007/s11071-018-4454-0

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