Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line

Abstract

We consider a weakly damped cubic nonlinear Schrodinger equation with Dirac interaction defect in a half line of \begin{document}$ \mathbb{R} $\end{document} . Endowed with artificial boundary condition at the point \begin{document}$ x = 0 $\end{document} , we discuss the global existence and uniqueness of solution of this equation by using Faedo–Galerkin method.