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- Title
Multi-soliton solutions of the three-level coupled Schrödinger Maxwell-Bloch equations via the Riemann-Hilbert approach.
- Authors
Li Peng; Huanhe Dong; Xiangrong Wang
- Abstract
In this paper, a study of the coupled Schrödinger Maxwell-Bloch equations, which described the propagation of two optical pulses in an optical medium with coherent three-level atoms, is presented via the Riemann-Hilbert approach. First, we performed a spectral analysis on the basis of Lax pair with the negative flow, and then the Jost function, scattering matrix, and their analytic and symmetric properties are given. Second, the Riemann-Hilbert problem is established successfully through a standard dressing procedure via the Riemann-Hilbert approach, and then the potential function related to the solution of the Riemann-Hilbert problem is reconstructed. By introducing the special matrix functions, we can transform the irregular Riemann-Hilbert problem into the regular one, which can be solved by the Plemelj formula. Finally, some applications are given to solve the Riemann-Hilbert problem without reflection for the coupled Schrödinger Maxwell-Bloch equation, and the multi-soliton solutions are obtained explicitly. Moreover, the dynamic behaviors of some soliton solutions are discussed graphically by choosing appropriate parameters.
- Subjects
SCHRODINGER equation; RIEMANN-Hilbert problems; S-matrix theory; MATRIX functions; SPECIAL functions; DARBOUX transformations; LAX pair
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 7, p5560
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9879