Spurious Four-Wave Mixing Processes in Generalized Nonlinear Schrödinger Equations

Numerical solutions of a nonlinear Schrödinger equation may suffer from the spurious four-wave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schrödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation has to be applied in a wide spectral window, e.g., because of the spectral broadening.