Local absorbing boundary conditions for two‐dimensional nonlinear Schrödinger equation with wave operator on unbounded domain

Abstract

The paper is devoted to designing the local absorbing boundary conditions for nonlinear Schrödinger equation with wave operator on unbounded domain in two dimensions. Introduce the artificial boundaries and find the appropriate absorbing boundary conditions for the original problem, which lead to a bounded computational domain. Constructing the local absorbing boundary conditions on the artificial boundaries, the original problem defined on unbounded domain is reduced to an initial boundary value problem on the bounded computational domain, which can be efficiently solved by the finite difference method. The stability of the reduced problem with the local absorbing boundary conditions is rigorously analyzed by introducing a series of auxiliary variables. The numerical results illustrate that the proposed approach is effective and feasible.