Propagation of nonlinear waves in disordered media

TL;DR

This paper investigates how nonlinear waves propagate in disordered media, revealing an exponential increase in solutions with sample size and exploring related phenomena like sensitivity and analogies to spin glasses.

Contribution

It demonstrates the exponential growth of solutions in nonlinear disordered media and discusses related effects and analogies, advancing understanding of wave behavior in complex systems.

Findings

Number of solutions increases exponentially with sample size.

Solutions are highly sensitive to external parameter changes.

Analogies to spin glass problems and time-dependent solutions are discussed.

Abstract

We study propagation of stationary waves in disordered non-linear media described by the non-linear Schroedinger equation and show that for given boundary conditions and a given coherent wave incident on a sample the number of solutions of the equation increase exponentially with the sample size. We also discuss the ballistic case, the sensitivity of the solutions to a change of external parameters, the similarity of this problem to the problem of spin glasses and time-dependent solutions.