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Breather degeneration and lump superposition for the $(3 + 1)$ $(3 + 1)$ -dimensional nonlinear evolution equation

Wei Tan

https://orcid.org/0000-0001-8894-8290

Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

College of Mathematics and Statistics, Jishou University, Jishou 416000, China

E-mail Address: tanwei1008@126.com

Corresponding author.

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and

Miao Li

College of Mathematics and Statistics, Jishou University, Jishou 416000, China

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https://doi.org/10.1142/S021798492150250XCited by:3 (Source: Crossref)

Abstract

This paper is devoted to the study of a (3 + 1)-dimensional generalized nonlinear evolution equation for the shallow-water waves. The breather solutions with different structures are obtained based on the bilinear form with perturbation parameters. Some new lump solitons are found in the process of studying the degradation behavior of breather solutions, and we also study general lump soliton, lumpoff solution and superposition phenomenon between lump soliton and breather solution. Besides, some theorems about the superposition between lump soliton and $N$ $N$ -soliton ( $N$ $N$ is a nonnegative integer) are given. Some examples, including lump- $N$ $N$ -exponential type, lump- $N$ $N$ -logarithmic type, higher-order lump-type $N$ $N$ -soliton, are given to illustrate the correctness of the theorems and corollaries described. Finally, some novel nonlinear phenomena, such as emergence of lump soliton, degeneration of breathers, fission and fusion of lumpoff, superposition of lump- $N$ $N$ -solitons, etc., are analyzed and simulated.

Keywords:

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