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Rational and semi-rational solutions of a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation

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Abstract

This paper mainly focuses on a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation which provides overwhelming support for studying the dynamics of high-dimensional nonlinear wave equations. The bilinear form of the equation is obtained based on the Hirota bilinear method, and the N-soliton solutions composed of the higher-order breather, periodic line wave and the mixed forms are constructed. Then, the rational and semi-rational solutions of the equation were acquired by using complex conjugate parameter relations and the long-wave limit method, which mainly consisted of high-order solitons, lumps, breathers and their mixed forms. We analyze the effect of the coefficients of space and time variables on the interaction of solutions to bilinear equations. By classifying these coefficients, we find that these coefficients change the interaction of the solutions by affecting the velocity, position, and trajectory of the waves. In order to describe the dynamics of solutions with different parameters more directly, the time evolution plots and density plots are presented, and the appearance and movement characteristics of the solutions are analyzed.

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Funding

The authors are grateful to the Editors and the Reviewers for their invaluable comments and suggestions, which have greatly improved the quality of this paper. The work is supported by the National Natural Science Foundation of China under Grant No.11975145.

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  1. Department of Mathematics, Shanghai University and Newtouch Center for Mathematics of Shanghai University, Shanghai, 200444, China

    Yingmin Yang, Tiecheng Xia & Tongshuai Liu

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  1. Yingmin Yang
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Yang, Y., Xia, T. & Liu, T. Rational and semi-rational solutions of a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation. Nonlinear Dyn 111, 16377–16394 (2023). https://doi.org/10.1007/s11071-023-08682-6

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