Pointwise second order convergence of structure-preserving scheme for the triple-coupled nonlinear Schrödinger equations

Abstract

In this paper, we present a finite difference scheme for the triple-coupled Schrödinger equations (T-CNLS) in optics. The T-CNLS is approximated by Crank-Nicolson scheme in time and finite difference method in space. Some mathematical characters are investigated, such as structure-preserving properties, unique solvability, convergence in L∞ norm. Some numerical examples are reported to illustrate the theoretical results.