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Novel resonant multi-soliton solutions and inelastic interactions to the (3 + 1)- and (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equations via the simplified linear superposition principle

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Abstract

In this paper, the resonant solitary waves to the (3 + 1)- and (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equations are exposed via the simplified linear superposition principle (LSP). Based on the related Hirota’s bilinear equations, the resonant multi-soliton solutions and the corresponding wave numbers are formally generated. Abundant inelastic interactions, i.e., fission and fusion of traveling N-solitary waves, are presented analytically and graphically. Besides, we show that the velocity resonance (VR) is not applicable to handle the (3 + 1)- and (4 + 1)-dimensional BLMP equations, due to that the dispersion relation is constructed as \(\omega = - k^{3}\). The results show that the simplified LSP provides enough freedom to construct resonant multi-soliton waves that has potential applications to a large variety of real physical phenomena.

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Acknowledgements

We are most grateful to the anonymous referees for the help in improving the original manuscript. And it is gratefully acknowledged that this work was supported by the Ministry of National Defense and the Ministry of Science and Technology, R. O. C., under Grant Numbers MOST 108-2221-E-344-002 and 109-2221-E-013-001.

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  1. Department of Aeronautics and Astronautics, Air Force Academy, Kaohsiung, 820, Taiwan, ROC

    Chun-Ku Kuo

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Kuo, CK. Novel resonant multi-soliton solutions and inelastic interactions to the (3 + 1)- and (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equations via the simplified linear superposition principle. Eur. Phys. J. Plus 136, 77 (2021). https://doi.org/10.1140/epjp/s13360-020-01062-8

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