A new absorbing layer approach for solving the nonlinear Schr?dinger equation

To simulate waves on unbounded domain, absorbing boundary conditions are usually needed to bound the computational domain and avoid boundary reflections as much as possible. In this paper, a new absorbing layer approach is presented to simulate the soliton propagation based on the cubic nonlinear Schrodinger (NLS) equation on unbounded domain, and a two-level finite difference scheme is constructed for solving this NLS problem. Both the analytical solution and the numerical solution are proved to be stable in L2-norm and l2-norm, respectively, and they decay exponentially in the absorbing (or called lossy) layers. Furthermore, the scheme is shown to be convergent with order O(t2 + h2), where t and h are the time step and grid size, respectively. Numerical examples are given to illustrate the method and verify its effectiveness.(c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a new absorbing layer approach for simulating soliton propagation on unbounded domain. A two-level finite difference scheme is used to solve the cubic nonlinear Schrodinger equation, and the stability and convergence of the scheme are analyzed. Numerical examples demonstrate the effectiveness of the method.