Darboux transformation and explicit solutions for the Kaup-Kupershmidt equation

Liu, Tongshuai; Xia, Tiecheng

doi:10.1088/1402-4896/acfa41

Cited by 2 publications

(1 citation statement)

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“…In the past decades, many excellent methods have been developed to construct exact solutions, such as the inverse scattering transform [20], Darboux transformation [21,22], Hirota bilinear theory [23,24], Lie group method [25], and so on. In recent years, Zhang [26][27][28] proposed a bilinear neural network method (BNNM) to find the exact solutions of NLPDEs.…”

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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