Inverse scattering transforms for the nonlocal Hirota–Maxwell–Bloch system. (22nd February 2023)

• Record Type: Journal Article
• Authors: An, Ling; Chen, Yiren; Ling, Liming
• Is Part Of: Journal of physics. Volume 56:Number 11(2023)
• Publication Date: 2023-02-22
• Subjects: nonlocal H-MB system -- Riemann–Hilbert problem -- inverse scattering transform -- soliton solution -- singularity -- asymptotic analysis; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/acbb45
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The Hirota and Maxwell–Bloch (H-MB) system is a mathematical model that can be used to describe the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By extending the parameter ω in the H-MB system to the complex domain, all the nonlocal forms of the H-MB system, including the reverse-space-time, complex reverse-space, complex reverse-time, complex reverse-space-time H-MB systems, are found. Then the Riemann–Hilbert problem of the nonlocal H-MB system is established to analyze the corresponding inverse scattering problem and construct the corresponding soliton solutions. When N = 1, the singularity of the one-soliton solutions of each nonlocal H-MB system is analyzed. When N = 2, we take the nonlocal reverse-space-time H-MB system and the nonlocal complex reverse-time H-MB system as examples, showing that a two-soliton can also be regarded as a superposition of two single-soliton in the nonlocal cases as | t | → ∞ .