Time-reversal focusing of an expanding soliton gas in disordered replicas

TL;DR

This paper studies how an expanding soliton gas can be time-reversed in disordered environments, revealing conditions under which focusing occurs despite disorder, using a novel approach combining information theory and spin glass concepts.

Contribution

It introduces a new class of reflectionless potentials for the defocusing nonlinear Schrödinger equation and analyzes time-reversal focusing in disordered media with a novel theoretical framework.

Findings

Time reversal focusing occurs for different disorder replicas under certain conditions.

Disorder varying on a short length scale allows for focusing despite environmental randomness.

A new class of reflectionless potentials describes the soliton gas dynamics.

Abstract

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.