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Interaction of multiple superposition solutions for the \((4 + 1)\)-dimensional Boiti-LeonManna-Pempinelli equation

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Abstract

Water wave is one of the most common phenomena in nature, and its involves mathematical modeling, aerodynamics, computer simulation, mechanical manufacturing, marine science and so on. Hence, the water wave dynamics of a (\(4+1\))-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid is investigated based on the Hirota bilinear method and homoclinic test method. We are aimed at constructing variable coefficient solutions to the equation under consideration. An existence theorem and corollary about superposition solutions of this equation are proved. The water wave dynamic behaviors of the reported results are presented by a careful choice of the arguments for the trigonometric and hyperbolic functions as the values of the variable coefficients. With the help of Mathematica, the effect of the variable coefficients on the reported results can be clearly seen by the three-dimensional profiles. Compared with the published studied, some completely new mathematical results and physical phenomena are presented in this paper. The results are beneficial to the study of water waves in fluid dynamics, and this technique has opened a new way to explain the physical properties of nonlinear phenomena.

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Acknowledgements

The authors deeply appreciate the anonymous reviewers for their helpful and constructive suggestions, which can help improve this paper further. This work is supported by the National Natural Science Foundation of China (Grant No. 11361040), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2020LH01008), the Graduate Students’ Scientific Research Innovation Fund Program of Inner Mongolia Normal University, China (Grant Nos. CXJJS19096, CXJJS20089), and the Graduate Research Innovation Project of Inner Mongolia Autonomous Region, China (Grant No. S20191235Z).

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  1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot, 010022, People’s Republic of China

    Peng-Fei Han & Taogetusang Bao

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Han, PF., Bao, T. Interaction of multiple superposition solutions for the \((4 + 1)\)-dimensional Boiti-LeonManna-Pempinelli equation. Nonlinear Dyn 105, 717–734 (2021). https://doi.org/10.1007/s11071-021-06603-z

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