Geodesic
Integrability of the~vector nonlinear Schr{\"o}dinger--Maxwell--Bloch equation and the~ Cauchy matrix approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 401-420

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We investigate the integrability and soliton solutions of the vector nonlinear Schrödinger–Maxwell–Bloch (VNLS–MB) equation. This equation is derived using the generalized $\bar \partial$-dressing method in a local $4\times 4$ matrix $\bar \partial$-problem. The vector nonlinear Schrödinger equation with self-consistent sources (VNLSSCS) is obtained and is proved to be equivalent to the VNLS–MB equation. Starting with Sylvester equation and the equivalence between the VNLS–MB and VNLSSCS equations, the $N$-soliton solutions of the VNLS–MB equation are successfully obtained by the Cauchy matrix approach. As an application, some interesting patterns of dynamical behavior are displayed.
Keywords: vector nonlinear Schrödinger–Maxwell–Bloch equation, zero-curvature equation, Cauchy matrix approach
Mots-clés : soliton solution. 
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     author = {Hui Zhou and Yehui Huang and Yuqin Yao},
     title = {Integrability of the~vector nonlinear {Schr{\"o}dinger--Maxwell--Bloch} equation and the~ {Cauchy} matrix approach},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {401--420},
     publisher = {mathdoc},
     volume = {215},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_3_a4/}
}
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Hui Zhou; Yehui Huang; Yuqin Yao. Integrability of the~vector nonlinear Schr{\"o}dinger--Maxwell--Bloch equation and the~ Cauchy matrix approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 401-420. http://geodesic.mathdoc.fr/item/TMF_2023_215_3_a4/