Global Existence and Long-time Behaviour of Nonlinear Equation of Schr\"odinger type

TL;DR

This paper proves global existence and analyzes the long-term behavior of solutions to a nonlinear Schrödinger equation with a generalized function coefficient, extending previous solvability results.

Contribution

It establishes a global solvability theorem for a nonlinear Schrödinger equation with a generalized function coefficient and investigates the solution's long-time behavior.

Findings

Proved global solvability of the nonlinear Schrödinger problem.

Analyzed the asymptotic behavior of solutions over time.

Extended solvability results to equations with generalized function coefficients.

Abstract

In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem with use of the general solvability theorem of the article [30]. Furthermore here is investigated also the behaviour of the solution of the studied problem.