Nonlinear wave-packet dynamics in a disordered medium

TL;DR

This paper develops an effective nonlinear diffusion model to describe complex wave-packet dynamics in disordered media, revealing phenomena like 'locked explosion' and 'diffusive' collapse applicable across various physical systems.

Contribution

It introduces a novel nonlinear diffusion equation as a unified framework for understanding wave dynamics in disordered nonlinear media.

Findings

Identification of 'locked explosion' phenomenon

Discovery of 'diffusive' collapse behavior

Applicability to photonic crystals and Bose-Einstein condensates

Abstract

In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and "diffusive" collapse. In this sense the equation can serve as a paradigmatic model, that can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.