Inverse scattering transforms for the nonlocal Hirota-Maxwell-Bloch system

作者：An, Ling; Chen, Yiren; Ling, Liming^*

来源：Journal of Physics A: Mathematical and Theoretical , 2023, 56(11): 115201.

DOI：10.1088/1751-8121/acbb45

• nonlocal H-MB system
• Riemann-Hilbert problem
• inverse scattering transform
• soliton solution
• singularity
• asymptotic analysis

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 omega 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 non local 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| -> infinity.