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Keywords:

  • Multiple scale approximation;
  • numerical experiments.

Abstract

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.