Minisymposium for Young Researchers - Abstract

Severing, Fenja

How numerics add to the instabilities of the generalised nonlinear Schrödinger equation

Nonlinear dispersive waves can experience modulational instability as described by the nonlinear Schrödinger equation (NLSE). Solved numerically by the split-step method (SSM), not only physical instabilities occur, but also unwanted numerical ones. Previous work considers how to avoid the numerical instability of the NLSE. Various setups in fibre optics are modelled by a generalised NLSE (GNLSE), for instance super continuum generation with input frequencies at zero dispersion wavelength. Here, we discuss a critical criterion for the correct spatial discretisation to avoid numerical instability in the context of the GNLSE. It can be seen that more accurate models featuring higher orders of dispersion come with a higher risk of including artefacts.