Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line

Abstract

Abstract We consider a nonlinear Schrödinger equation with Dirac interaction defect. Moreover, non-standard boundary conditions are introduced in connection to the behavior of the solutions. First, we prove that this kind of Schrödinger equation can be characterized by an autonomous dynamical system. Then, based on this result, we show that such an equation possesses a maximal compact attractor in the weak topology of H 1 $\mathbf{H}^{\mathbf{1}}$ .

Keywords

• damped nonlinear Schrödinger equation
• Dirac interaction defect
• artificial boundary condition
• autonomous dynamical system
• global attractor