The Darboux transformation for the coupled Hirota equation

Starting from local coupled Hirota equations, we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz–Kaup–Newell–Segur scattering problem. The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair. By Lax pair, an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found. The solutions with specific properties are distinct from those of the local Hirota equation. In order to further describe the properties and the dynamic features of the solutions explicitly, several kinds of graphs are depicted.

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“…( 1) when u = −v * , and v * denotes the complex conjugate of v. The linear spectral problem (i.e., Lax pair) of Eqs. ( 4) is expressed by [23] ψ…”

Section: Integrable Nonlocal Hirota Equationmentioning

confidence: 99%

Darboux transformation and soliton solutions of a nonlocal Hirota equation

2022

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“…where α(t), β(t) are variable coefficients. Hirota equation is an important model which can be used to describe many kinds of nonlinear phenomena or mechanisms in the fields of physics, optical fibers, electric communication and other engineering sciences [30]. It is valuable to study the Hirota equation with variable coefficients to solve the inhomogeneity problem in optical fiber and plasma [31], while nonlocal reduction will make the solution of the system more complicated [32].…”

Section: Introductionmentioning

confidence: 99%

Generalized perturbation (n, N − n) fold Darboux transformation for a nonlocal Hirota equation with variable coefficients

Zhao,

Zhaqilao

2024

Phys. Scr.

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In this paper, a nonlocal Hirota equation with variable coeﬃcients is investigated by applying the generalized perturbation (n, N − n) fold Darboux transformation method and Taylor expansion method. Multi-soliton solutions are obtained when the seed solution is trivial, and multi-soliton solutions, multi-breather solutions, high-order rogue wave solutions and their interaction solutions are obtained when the seed solution is a plane wave solution. Especially, we get the interaction solution of soliton, breather and rogue wave solution. In addition, by choosing appropriate parameters, the dynamic behaviors of the obtained solution are explored.

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“…where γ and ρ are arbitrary constants, and δ (t) is an arbitrary function of t. In the literature, [28] Zhang et al followed the AKNS procedure to construct Lax pairs with spectral parameters and obtained the coupled Hirota equation. In this paper, we construct the nonlocal Hirota equation with variable coefficients by means of modifying its Lax pair, and the symmetric reduction.…”

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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The Darboux transformation for the coupled Hirota equation

Cited by 7 publications

References 10 publications

Darboux transformation and soliton solutions of a nonlocal Hirota equation

Darboux transformation and soliton solutions of a nonlocal Hirota equation

Generalized perturbation (n, N − n) fold Darboux transformation for a nonlocal Hirota equation with variable coefficients

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

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