Integration of the nonlinear Schrödinger equation with a self-consistent source and nonzero boundary conditions

2023/01/11 by Anvar Reyimberganov, Reyimberganov, Anvar
Mathematics · Physics and Astronomy · #34L25 #34M46 #35Q41 #35R30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2301.04588

openalex publication_date 2023/01/11 · openalex created_date 2023/01/13 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the study of the defocusing nonlinear Schrödinger equation with a self-consistent source and nonzero boundary conditions by the method of the inverse scattering problem. In cases where the source consists of a combination of eigenfunctions of the corresponding spectral problem for the Zakharov-Shabat system, the complete integrability of the nonlinear Schrödinger equation is investigated. Namely, the evolutions of the scattering data of the self-adjoint Zakharov-Shabat system, whose potential is a solution of the defocusing nonlinear Schrödinger equation with a self-consistent source, are obtained.

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