Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity



The Nonlinear Schrödinger (NLS) equation is a universal amplitude equation which can be derived for the description of small spatio-temporal modulations of an underlying carrier wave. The validity of this approximation for general dispersive wave systems possessing a quasilinear quadratic nonlinearity is an open problem that has remained unsolved for more than four decades. We report results on a systematic numerical simulation of such a quasilinear wave equation which strongly support the validity claim.