التفاصيل البيبلوغرافية
| العنوان: |
Multi-soliton solutions of the three-level coupled Schrödinger Maxwell-Bloch equations via the Riemann-Hilbert approach. |
| المؤلفون: |
Li Peng, Huanhe Dong, Xiangrong Wang |
| المصدر: |
Mathematical Methods in the Applied Sciences; 5/15/2024, Vol. 47 Issue 7, p5560-5575, 16p |
| مصطلحات موضوعية: |
SCHRODINGER equation, RIEMANN-Hilbert problems, S-matrix theory, MATRIX functions, SPECIAL functions, DARBOUX transformations, LAX pair |
| مستخلص: |
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. [ABSTRACT FROM AUTHOR] |
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