Numerical solution of nonlinear Schrödinger equation with damping term on unbounded domain

Abstract

The artificial boundary method is applied to numerically solve the nonlinear Schrödinger equation with damping term on unbounded domain. A novel transformation is developed to eliminate the troublesome damping term, which yields the difficulty to design the artificial boundary conditions. The artificial boundary conditions are investigated to reduce the original problem into an initial boundary value problem, based on the idea of operator splitting approach. The stability of the reduced problem is analyzed by the energy estimation. The accuracy and effectiveness of the proposed method are verified by numerical examples.