The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method

doi:10.1088/1674-1056/adce9c

中国物理B ›› 2025, Vol. 34 ›› Issue (9): 90202-090202.doi: 10.1088/1674-1056/adce9c

The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method

Xin Wang(王昕)† and Zhi-Hui Zhang(张智辉)

Department of Fundamentals, Air Force Engineering University, Xi'an 710051, China

收稿日期:2025-02-21 修回日期:2025-03-20 接受日期:2025-04-21 出版日期:2025-08-21 发布日期:2025-09-09
通讯作者: Xin Wang E-mail:wangxin8058@163.com
基金资助:
Project supported by Shaanxi Scholarship Council of China (Grant No. 2021-030), the Youth Scientific Research Project of Shaanxi Province, China (Grant No. 202103021223060), and the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. S2025-JC-QN-1854).

The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method

Xin Wang(王昕)† and Zhi-Hui Zhang(张智辉)

Department of Fundamentals, Air Force Engineering University, Xi'an 710051, China

Received:2025-02-21 Revised:2025-03-20 Accepted:2025-04-21 Online:2025-08-21 Published:2025-09-09
Contact: Xin Wang E-mail:wangxin8058@163.com
Supported by:
Project supported by Shaanxi Scholarship Council of China (Grant No. 2021-030), the Youth Scientific Research Project of Shaanxi Province, China (Grant No. 202103021223060), and the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. S2025-JC-QN-1854).

摘要/Abstract

摘要： In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing, we study a class of high-order three-component Hirota equations by the Riemann-Hilbert method. Under zero boundary conditions and given initial conditions $q_{j}(x,0)$, the $N$-soliton solutions of the equations are obtained by constructing and solving Riemann-Hilbert problems based on matrix spectral problem. Specifically, we discuss the cases of $N=1, 2$, analyze the dynamical properties of $1$-soliton and $2$-soliton solutions through numerical simulations, and summarize the effect of integrable perturbations and spectral parameters on soliton motion.

关键词: coupled Hirota equation, soliton solutions, Riemann-Hilbert problem, matrix spectral problem

Abstract: In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing, we study a class of high-order three-component Hirota equations by the Riemann-Hilbert method. Under zero boundary conditions and given initial conditions $q_{j}(x,0)$, the $N$-soliton solutions of the equations are obtained by constructing and solving Riemann-Hilbert problems based on matrix spectral problem. Specifically, we discuss the cases of $N=1, 2$, analyze the dynamical properties of $1$-soliton and $2$-soliton solutions through numerical simulations, and summarize the effect of integrable perturbations and spectral parameters on soliton motion.

Key words: coupled Hirota equation, soliton solutions, Riemann-Hilbert problem, matrix spectral problem

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.30.Ik (Integrable systems) 02.40.Xx (Singularity theory)

Xin Wang(王昕) and Zhi-Hui Zhang(张智辉). The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method[J]. 中国物理B, 2025, 34(9): 90202-090202.

Xin Wang(王昕) and Zhi-Hui Zhang(张智辉). The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method[J]. Chin. Phys. B, 2025, 34(9): 90202-090202.

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The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method

The N-soliton solutions of the three-component coupled nonlinear Hirota equations based on Riemann-Hilbert method

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