On the damped nonlinear Schödinger equation with delta functions as initial data

Abstract

In this paper, we consider the Cauchy problem for the damped nonlinear Schrödinger equation with superposed delta functions as initial data. The aim of this paper is to study the influence of nonlinearity and damping (absorption) on the solution. The case where the nonlinearity makes the solution unstable is of special interest, because the dissipative nature from the damping comes into play in this case.