Geodesic
Soliton solutions of the~negative-order nonlinear Schr\"{o}dinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 263-273

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We discuss the integration of the Cauchy problem for the negative-order nonlinear Schrödinger equation in the class of rapidly decreasing functions via the inverse scattering problem method. In particular, we obtain the time dependence of scattering data of the Zakharov–Shabat system with the potential that is a solution of the considered problem. We give an explicit representation of the one-soliton solution of the negative-order nonlinear Schrödinger equation based on the obtained results.
Keywords: negative-order nonlinear Schrödinger equation, recursion operator, inverse scattering transform, scattering data, Zakharov–Shabat system
Mots-clés : soliton. 
@article{TMF_2024_219_2_a4,
     author = {G. U. Urazboev and I. I. Baltaeva and A. K. Babadjanova},
     title = {Soliton solutions of the~negative-order nonlinear {Schr\"{o}dinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {263--273},
     publisher = {mathdoc},
     volume = {219},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a4/}
}
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G. U. Urazboev; I. I. Baltaeva; A. K. Babadjanova. Soliton solutions of the~negative-order nonlinear Schr\"{o}dinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 263-273. http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a4/