Improved effective linearization of nonlinear Schr\"odinger waves by increasing nonlinearity

TL;DR

This paper identifies a family of nonlinear Schrödinger waves that, with increasing amplitude, behave more like weakly coupled plane waves, revealing a new effective linearization mechanism.

Contribution

It introduces a robust family of disordered NLS waves where higher amplitudes lead to weaker wave coupling, enhancing understanding of nonlinear wave dynamics.

Findings

Energy in wave coupling decreases with amplitude

Waves evolve as weakly coupled plane waves at high amplitudes

Disordered wave family is robust over long times

Abstract

From among the waves whose dynamics are governed by the nonlinear Schr\"odinger (NLS) equation, we find a robust, spatiotemporally disordered family, in which waves initialized with increasing amplitudes, on average, over long time scales, effectively evolve as ever more weakly coupled collections of plane waves. In particular, the relative amount of energy contained in their coupling decays to zero with increasing wave amplitude.