Fission and annihilation phenomena of breather/rogue waves and interaction phenomena on nonconstant backgrounds for two KP equations

Lv, Na; Yue, Yichao; Zhang, Runfa; Yuan, Xue Gang; Wang, Ran

doi:10.1007/s11071-023-08329-6

Cited by 4 publications

(1 citation statement)

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“…Theoretically, the dimension of independent variable input to the network model can be arbitrary, so this method may be more suitable for solving high-dimensional equations, and has attracted great attention from scholars. Lv [29] obtained a series of nonlinear phenomena of breather/rogue waves and interaction phenomena on nonconstant backgrounds for two KP equations by using symmetry analysis and BNNM. Ma [30] employed BNNM to obtain some new exact analytical solutions to the (2+1)-dimensional Ito equation.…”

Section: Introductionmentioning

confidence: 99%

Various nonlinear characteristics of breather/rogue waves and controllable interaction phenomena for a new KdV equation with variable coeffcients

Lv,

Yue,

Zhang

et al. 2024

Phys. Scr.

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In this paper, we investigate and analyze various nonlinear phenomena of a new (2+1)-dimensional KdV equation with variable coefficients, and successfully obtain breather/rogue wave solutions and interaction solutions of the KdV equation by using the bilinear neural network method and symmetry transformation. Subsequently, we analyze the dynamical characteristics and evolution process of these obtained solutions through the 3-D animations, and find a series of interesting nonlinear phenomena concerning breather/rogue waves, such as fission, regeneration, annihilation, collision, and controllable interaction phenomena on nonzero backgrounds. This paper provides a more intuitive understanding for the nonlinear phenomena of these obtained solutions, and these nonlinear phenomena have potential application value in fluid dynamics, elastic mechanics and other fields of nonlinear science.

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Section: Introductionmentioning

confidence: 99%