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

Abstract

<p style='text-indent:20px;'>We consider a weakly damped cubic nonlinear Schrödinger equation with Dirac interaction defect in a half line of <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R} $\end{document}</tex-math></inline-formula>. Endowed with artificial boundary condition at the point <inline-formula><tex-math id="M2">\begin{document}$ x = 0 $\end{document}</tex-math></inline-formula>, we discuss the global existence and uniqueness of solution of this equation by using Faedo–Galerkin method.</p>