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Novel evolutionary behaviors of localized wave solutions and bilinear auto-Bäcklund transformations for the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation

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Abstract

Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In the present paper, we first deduce five kinds of bilinear auto-Bäcklund transformations of the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation starting from the specially exchange identities of the Hirota bilinear operators; then, we construct the N-soliton solutions and several new structures of the localized wave solutions which are studied by using the long wave limit method and the complex conjugate condition technique. In addition, the propagation orbit, velocity and extremum of the first-order lump solution on (x, y)-plane are studied in detail, and seven mixed solutions are summarized. Finally, the dynamical behaviors and physical properties of different localized wave solutions are illustrated and analyzed. It is hoped that the obtained results can provide a feasibility analysis for water wave dynamics.

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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 was supported by the National Natural Science Foundation of China (Grant Nos. 11371326, 11975145 and 12271488).

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  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Peng-Fei Han, Yi Zhang & Chi-Hui Jin

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Han, PF., Zhang, Y. & Jin, CH. Novel evolutionary behaviors of localized wave solutions and bilinear auto-Bäcklund transformations for the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation. Nonlinear Dyn 111, 8617–8636 (2023). https://doi.org/10.1007/s11071-023-08256-6

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