This article is cited in 9 papers

Soliton solutions of the negative-order nonlinear Schrödinger equation

G. U. Urazboev^ab, I. I. Baltaeva^a, A. K. Babadjanova<sup>b

a</sup> Urgench State University, Urgench, Uzbekistan
^b Khorezm Branch of the Romanovsky Institute of Mathematics, Uzbekistan Academy of Science, Urgench, Uzbekistan

Abstract: 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, soliton.

Received: 06.12.2023
Revised: 23.01.2024

DOI: 10.4213/tmf10652

 English version: Theoretical and Mathematical Physics, 2024, 219:2, 761–769

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