An effective theory of pulse propagation in a nonlinear and disordered medium in two dimensions

TL;DR

This paper develops a nonlinear diffusion theory to describe pulse propagation in disordered, nonlinear media, revealing novel phenomena like 'locked explosion' and 'diffusive' collapse applicable to systems like photonic crystals and Bose-Einstein condensates.

Contribution

It introduces a simplified nonlinear diffusion equation that captures complex pulse behaviors in disordered nonlinear systems, unifying different physical contexts.

Findings

Identification of 'locked explosion' phenomenon

Discovery of 'diffusive' collapse behavior

Applicability to photonic crystals and Bose-Einstein condensates

Abstract

We develop an effective theory of pulse propagation in a nonlinear {\it 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. The equation 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.