Failure of amplitude equations

Abstract

The nonlinear Schrodinger (NLS) equation is an example of a universal nonlinear model that describes many physical nonlinear systems. The equation can be applied to hydrodynamics, nonlinear optics, nonlinear acoustics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. It describes small modulations in time and space of a spatially and temporally oscillating wave packet advancing in a laboratory frame. It has first been derived for the so called water wave problem in 1968 and the proof that it makes correct predictions has been recently the subject of intensive research.