Geodesic
Inverse scattering transform and soliton classification of
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 3, pp. 323-341

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: higher-order nonlinear Schrödinger–Maxwell–Bloch equation, Riemann–Hilbert method
Mots-clés : soliton solution. 
@article{TMF_2020_203_3_a0,
     author = {Zhi-Qiang Li and Shou-Fu Tian and Wei-Qi Peng and Jin-Jie Yang},
     title = {Inverse scattering transform and soliton classification of},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--341},
     publisher = {mathdoc},
     volume = {203},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_203_3_a0/}
}
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Zhi-Qiang Li; Shou-Fu Tian; Wei-Qi Peng; Jin-Jie Yang. Inverse scattering transform and soliton classification of. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 3, pp. 323-341. http://geodesic.mathdoc.fr/item/TMF_2020_203_3_a0/