Existence and stability results on a class of Non Linear Schroedinger Equations in bounded domains with Dirichlet boundary conditions

TL;DR

This paper establishes existence and stability of solutions resembling solitary waves for a class of nonlinear Schrödinger equations within bounded domains with Dirichlet boundary conditions.

Contribution

It provides new existence and stability results for nonlinear Schrödinger equations with bounded nonlinearity and Dirichlet conditions, highlighting solitary wave features.

Findings

Existence of solutions in bounded domains with Dirichlet boundary conditions.

Stability of solutions exhibiting solitary wave characteristics.

Solutions demonstrate specific stability properties under the studied conditions.

Abstract

Existence of solution and stability results on a class of Non Linear Schroedinger type equations with a bounded nonlinearity are obtained, for a bounded domain and with Dirichlet boundary conditions. The kind of stability under discussion shows that the corresponding solution exhibits features of a solitary wave type.