Finite Difference Solution Methods for a System of the Nonlinear Schrödinger Equations - Kurtinaitis, A.; Ivanauskas, F. (Nonlinear Analysis: Modelling and Control, 2004)
This paper investigates finite difference schemes for solving a system of the nonlinear Schrödinger (NLS) equations. Several types of schemes, including explicit, implicit, Hopscotch-type and Crank-Nicholson-type are defined. Cubic spline interpolation is used for solving time-shifting part of equations. The numerical results of the different solution methods are compared using two analytical invariant properties.
Keywords: finite-difference; scheme comparison; numerical simulation; nonlinear; Schrödinger equation; second harmonics generation