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

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.

arXiv comment7 Pages, 6 Figures

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• Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves
• Resonant radiation shed by dispersive shock waves
• Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation
• Nonlinear Gamow vectors, shock waves and irreversibility in optically nonlocal media
• Generalized hypergeometric solutions of the Heun equation