A perfectly matched layer approach to the nonlinear Schrödinger wave equations

Authors:
Chunxiong Zheng
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

Absorbing boundary conditions (ABCs) are generally required for simulating waves in unbounded domains. As one of those approaches for designing ABCs, perfectly matched layer (PML) has achieved great success for both linear and nonlinear wave equations. In this paper we apply PML to the nonlinear Schrodinger wave equations. The idea involved is stimulated by the good performance of PML for the linear Schrodinger equation with constant potentials, together with the time-transverse invariant property held by the nonlinear Schrodinger wave equations. Numerical tests demonstrate the effectiveness of our PML approach for both nonlinear Schrodinger equations and some Schrodinger-coupled systems in each spatial dimension.