Various exact analytical solutions of a variable-coefficient Kadomtsev–Petviashvili equation

Liu, Jian‐Guo; Zhu, Wen‐Hui

doi:10.1007/s11071-020-05629-z

Cited by 20 publications

(1 citation statement)

References 53 publications

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“…Therefore, research of variable coefficient equations is of even more physical significance. [29][30][31] When δ (t) = 1, Eq. ( 1) is the third flow of the NLS structure, and this nonlinear evolution equation can be used to describe important models in physics, fibre optics and other engineering disciplines.…”

Section: Introductionmentioning

confidence: 99%

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

Liu 刘,

Yan 闫,

Jin 金

et al. 2023

Chinese Phys. B

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This article presents the construction of a nonlocal Hirota equation with variable coefficient and its Darboux transformation. Using zero-seed solutions, 1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation, along with the expression for N-soliton solutions. The influence of coefficient functions on the solutions is investigated by choosing different coefficient functions, and the dynamics of the solutions are analyzed. For the first time, this article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations. The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

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Section: Introductionmentioning

confidence: 99%