Global weak solutions of an initial-boundary value problem on a half-line for the higher order nonlinear Schr\"{o}dinger equation

TL;DR

This paper investigates the existence and uniqueness of global weak solutions for a higher order nonlinear Schrödinger equation on a half-line, considering specific boundary conditions and nonlinearities.

Contribution

It provides new results on global weak solutions for a higher order nonlinear Schrödinger equation with boundary conditions and nonlinearities.

Findings

Existence of global weak solutions established.

Uniqueness and continuous dependence proven.

Results applicable to specific boundary conditions and nonlinearities.

Abstract

An initial-boundary value problem with one boundary condition is considered for the higher order nonlinear Schr\"odinger equation. It is assumed that either the boundary condition is homogeneous or the nonlinearity in the equation is quadratic. Results on existence, uniqueness and continuous dependence on input data of global weak solutions are obtained.