Some new soliton solutions and dynamical behaviours of (3+1)-dimensional Jimbo-Miwa equation

Li, Meng-Jun; Dai, Hou-Ping; Wei, Xuedan; Tan, Wei

doi:10.1080/00207160.2021.1998468

Cited by 5 publications

(1 citation statement)

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“…With the development of NPDE research, a large number of theoretical and application achievements appear constantly, such as the Hirota bilinear approach [1], the long-wave limit technique [2], the inverse scattering approach [3] as well as the Darboux transformation [4], etc. At the same time, Many new solitary waves of NPDE, such as high-breather, kink-shaped soliton, double breathers, high-order lump and high-order rogue wave, attract a lot of attention [5][6][7][8][9][10][11][12]. Unlike soliton with stable structures, lump and breather waves are localized, unstable, and unpredictable in space and can be used to prevent natural disasters.…”

Section: Introductionmentioning

confidence: 99%

Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

Wang,

Wei,

Huang

2024

Phys. Scr.

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In this paper, the trajectory equations of 1-lump before and after collision with high-order solitons and the degradation of some novel breather waves are studied in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation(gCBS). Firstly, we derive N-solitons for the gCBS equation by the Hirota bilinear form. With the help of N-solitons, we obtain M-lump and high-order breather based on the long-wave limit technique and the parametric conjugate method. Secondly, we construct some hybrid waves, such as the hybrid wave between breather and lump. Thirdly, the interaction phenomenon of lump-N-solitonsis investigated, and the theory of its existence is given and proved. Besides, the different degeneracies of double and single breather are discussed. Finally, we also present a large number of two-dimensional and three-dimensional images to better illustrate these nonlinear evolutionary behaviors.

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