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Dynamical behavior of multiwave interaction solutions for the (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation

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Abstract

The (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation is used to simulate the evolution of shallow water waves with weakly nonlinear restorative forces and waves in a strong magnetic medium, as well as ion acoustic waves and stratified ocean internal waves in incompressible fluids. The bilinear representation, Bäcklund transformation, Lax pair and infinite conservation laws of the equation are systematically constructed by using the Bell polynomial method. Based on the Hirota bilinear method and some propositions, several new analytic solutions are studied, including the hybrid solutions among the lump waves and periodic waves, mixed solutions between the lump waves and periodic waves, mixed solutions between periodic waves. The dynamic behaviors of these analytical solutions are studied by means of three-dimensional diagrams, and some new structures and properties of waves are found. The research results provide a new method for us to explore the model. The obtained results can be widely used to report various interesting physical phenomena in the field of shallow water waves, fluid mechanics, ocean dynamics and other similar fields.

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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 has been supported by the National Natural Science Foundation of China (Grant No. 11361040), the Fundamental Research Funds for the Inner Mongolia Normal University, China (Grant No. 2022JBZD011), 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 No. CXJJS19096, No. 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

  2. Center for Applied Mathematics Inner Mongolia, Huhhot, 010022, People’s Republic of China

    Peng-Fei Han & Taogetusang Bao

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Han, PF., Bao, T. Dynamical behavior of multiwave interaction solutions for the (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation. Nonlinear Dyn 111, 4753–4768 (2023). https://doi.org/10.1007/s11071-022-08097-9

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