Darboux transformation and soliton solutions of a nonlocal Hirota equation

doi:10.1088/1674-1056/ac11e9

中国物理B ›› 2022, Vol. 31 ›› Issue (2): 20401-020401.doi: 10.1088/1674-1056/ac11e9

Darboux transformation and soliton solutions of a nonlocal Hirota equation

Yarong Xia(夏亚荣)^1,2, Ruoxia Yao(姚若侠)^1,†, and Xiangpeng Xin(辛祥鹏)³

1 School of Computer Science, Shaanxi Normal University, Xi'an 710062, China;
2 School of Information and Engineering, Xi'an University, Xi'an 710065, China;
3 School of Mathematical Sciences, Liaocheng University, Liaocheng 252029, China

收稿日期:2021-06-11 修回日期:2021-06-28 接受日期:2021-07-07 出版日期:2022-01-13 发布日期:2022-01-13
通讯作者: Ruoxia Yao E-mail:rxyao@snnu.edu.cn
基金资助:
The project was supported by the National Natural Science Foundation of China (Grant Nos. 12001424, 11471004, and 11775047), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JZ-21), the Chinese Post doctoral Science Foundation (Grant No. 2020M673332), the Research Award Foundation for Outstanding Young Scientists of Shandong Province, China (Grant No. BS2015SF009), and the Three-Year Action Plan Project of Xi'an University (Grant No. 21XJZZ0001-01).

Darboux transformation and soliton solutions of a nonlocal Hirota equation

Yarong Xia(夏亚荣)^1,2, Ruoxia Yao(姚若侠)^1,†, and Xiangpeng Xin(辛祥鹏)³

1 School of Computer Science, Shaanxi Normal University, Xi'an 710062, China;
2 School of Information and Engineering, Xi'an University, Xi'an 710065, China;
3 School of Mathematical Sciences, Liaocheng University, Liaocheng 252029, China

Received:2021-06-11 Revised:2021-06-28 Accepted:2021-07-07 Online:2022-01-13 Published:2022-01-13
Contact: Ruoxia Yao E-mail:rxyao@snnu.edu.cn
Supported by:
The project was supported by the National Natural Science Foundation of China (Grant Nos. 12001424, 11471004, and 11775047), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JZ-21), the Chinese Post doctoral Science Foundation (Grant No. 2020M673332), the Research Award Foundation for Outstanding Young Scientists of Shandong Province, China (Grant No. BS2015SF009), and the Three-Year Action Plan Project of Xi'an University (Grant No. 21XJZZ0001-01).

摘要/Abstract

摘要： 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.

关键词: nonlocal Hirota equation, Darboux transformation, Lax pair, soliton soultion

Abstract: 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.

Key words: nonlocal Hirota equation, Darboux transformation, Lax pair, soliton soultion

中图分类号: (Partial differential equations)

02.30.Jr

04.20.Jb (Exact solutions) 11.10.Lm (Nonlinear or nonlocal theories and models)

Yarong Xia(夏亚荣), Ruoxia Yao(姚若侠), and Xiangpeng Xin(辛祥鹏). Darboux transformation and soliton solutions of a nonlocal Hirota equation[J]. 中国物理B, 2022, 31(2): 20401-020401.

Yarong Xia(夏亚荣), Ruoxia Yao(姚若侠), and Xiangpeng Xin(辛祥鹏). Darboux transformation and soliton solutions of a nonlocal Hirota equation[J]. Chin. Phys. B, 2022, 31(2): 20401-020401.

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Darboux transformation and soliton solutions of a nonlocal Hirota equation

Darboux transformation and soliton solutions of a nonlocal Hirota equation

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