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 Schrödinger equation.
- Publication:
-
Physical Review A
- Pub Date:
- May 2011
- DOI:
- 10.1103/PhysRevA.83.053846
- arXiv:
- arXiv:1104.1886
- Bibcode:
- 2011PhRvA..83e3846F
- Keywords:
-
- 42.65.Tg;
- 03.75.Lm;
- 05.10.-a;
- 47.35.Jk;
- Optical solitons;
- nonlinear guided waves;
- Tunneling Josephson effect Bose-Einstein condensates in periodic potentials solitons vortices and topological excitations;
- Computational methods in statistical physics and nonlinear dynamics;
- Wave breaking;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 7 Pages, 6 Figures