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

doi:10.1088/1674-1056/acf703

中国物理B ›› 2023, Vol. 32 ›› Issue (12): 120401-120401.doi: 10.1088/1674-1056/acf703

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

Jinzhou Liu(刘锦洲), Xinying Yan(闫鑫颖), Meng Jin(金梦), and Xiangpeng Xin(辛祥鹏)^†

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

收稿日期:2023-06-22 修回日期:2023-09-05 接受日期:2023-09-06 出版日期:2023-11-14 发布日期:2023-11-27
通讯作者: Xiangpeng Xin E-mail:xinxiangpeng@lcu.edu.cn
基金资助:
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).

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

Jinzhou Liu(刘锦洲), Xinying Yan(闫鑫颖), Meng Jin(金梦), and Xiangpeng Xin(辛祥鹏)^†

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Received:2023-06-22 Revised:2023-09-05 Accepted:2023-09-06 Online:2023-11-14 Published:2023-11-27
Contact: Xiangpeng Xin E-mail:xinxiangpeng@lcu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: infinite conservation laws, nonlocal Hirota equation with variable coefficient, soliton solutions, Darboux transformation

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.

Key words: infinite conservation laws, nonlocal Hirota equation with variable coefficient, soliton solutions, Darboux transformation

中图分类号: (Exact solutions)

04.20.Jb

05.45.Yv (Solitons) 02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)

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[J]. 中国物理B, 2023, 32(12): 120401-120401.

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Darboux transformation, infinite conservation laws, and exact solutions for the 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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