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

doi:10.1088/1674-1056/acf703

Abstract This article presents the construction of a nonlocal Hirota equation with variable coefficients 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. Influence of coefficients that are taken as a function of time instead of a constant, i.e., coefficient function δ(t), on the solutions is investigated by choosing the coefficient function δ(t), and the dynamics of the solutions are analyzed. 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.

Keywords: infinite conservation laws nonlocal Hirota equation with variable coefficient soliton solutions Darboux transformation

Received: 22 June 2023
Revised: 05 September 2023
Accepted manuscript online: 06 September 2023

PACS:	04.20.Jb	(Exact solutions)
	05.45.Yv	(Solitons)
	02.30.Ik	(Integrable systems)
	02.30.Jr	(Partial differential equations)

Fund: This work was supported by the National Natural Science Foundation of China (Grant No.11505090), Liaocheng University Level Science and Technology Research Fund (Grant No.318012018), Discipline with Strong Characteristics of Liaocheng University--Intelligent Science and Technology (Grant No.319462208), Research Award Foundation for Outstanding Young Scientists of Shandong Province (Grant No.BS2015SF009), and the Doctoral Foundation of Liaocheng University (Grant No.318051413).

Corresponding Authors: Xiangpeng Xin
E-mail: xinxiangpeng@lcu.edu.cn

Cite this article:

Jinzhou Liu(刘锦洲), Xinying Yan(闫鑫颖), Meng Jin(金梦), and Xiangpeng Xin(辛祥鹏) Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients 2023 Chin. Phys. B 32 120401

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

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