High-order split-step exponential methods for solving coupled nonlinear Schrodinger equations

Abstract

Numerical integration schemes for coupled time-dependent nonlinear Schrodinger equations are examined using exponential splitting step methods. Exponentiation of the nonlinear potential term is reduced to the exponential of a kinetic energy term which can be calculated by fast Fourier transforms. High-order iteration schemes involving a minimum number of product operators are shown to yield highly accurate amplitude and phase. These new splitting methods are shown to be highly efficient both with respect to accuracy and integration time.