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

doi:10.1088/1674-1056/adce9c

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.

Keywords: coupled Hirota equation soliton solutions Riemann-Hilbert problem matrix spectral problem

Received: 21 February 2025
Revised: 20 March 2025
Accepted manuscript online: 21 April 2025

PACS:	02.60.Cb	(Numerical simulation; solution of equations)
	02.30.Ik	(Integrable systems)
	02.40.Xx	(Singularity theory)

Fund: 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).

Corresponding Authors: Xin Wang
E-mail: wangxin8058@163.com

Cite this article:

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 2025 Chin. Phys. B 34 090202

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

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