Inverse scattering transform and soliton classification of

Zhi-Qiang Li   ; Shou-Fu Tian   ; Wei-Qi Peng   ; Jin-Jie Yang

Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 3, pp. 323-341

Résumé

We investigate higher-order nonlinear Schrödinger–Maxwell–Bloch equations using the Riemann–Hilbert method. We perform a spectral analysis of the Lax pair and construct a Riemann–Hilbert problem according to the spectral analysis. As a result, we obtain three types of multisoliton solutions. Based on the analytic solution and with a choice of corresponding parameter values, we obtain solutions of the breather type and a bell-shaped solution and find an interesting phenomenon of the collision of two soliton solutions. We hope that these results can be useful in modeling the wave propagation of a nonlinear optical field in an erbium-doped fiber medium.

Détail

Keywords: higher-order nonlinear Schrödinger–Maxwell–Bloch equation, Riemann–Hilbert method
Mots-clés : soliton solution.

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