Resonance Nls Solitons as Black Holes in Madelung Fluid

A new resonance version of NLS equation is found and embedded to the reactiondiffusion system, equivalent to the anti-de Sitter valued Heisenberg model, realizing a particular gauge fixing condition of the Jackiw-Teitelboim gravity. The space-time points where dispersion change the sign correspond to the event horizon, and the soliton solutions to the AdS black holes. The soliton with velocity bounded above describes evolution on the hyperboloid with nontrivial winding number and create under collisions the resonance states with a specific life time. 1. Resonance NLS equation. The connection between black hole physics and the theory of supersonic acoustic flow was established by Unruh and has been developed to investigate the Hawking radiation and other phenomena for understanding quantum gravity. Recently, the similar idea for simulation of quantum effects related to event horizons and ergoregions but in superfluids, which in contrast to the usual liquids allow nondissipative motion of the flow, was proposed. In this case a ”superluminally” moving inhomogeneity of the order parameter like solitons, provides black holes like quasi-equilibrium states, exhibiting an event horizon. Although Jacobson and Volovik considered a simplified profile of soliton and mentioned unimportance of exact structure of the solution, an exactly soluble model of solitons related to black holes allows one to describe the scattering process of black holes and corresponding quantum phenomena. Very recently, some attempt was done to describe solitons of integrable models like the Liouville, the Sine-Gordon 5,15 and the ReactionDiffusion system, as black holes of Jackiw-Teitelboim (JT) gravity. In the last paper the scattering of two identical soliton-like structures called dissipatons, relating to the black holes and creating the metastable state was considered. Continuing in this direction, in the present paper we present a new integrable version of the Nonlinear Schrödinger equation (NLS) in 1+1 dimensions, admitting solitons with a rich resonance scattering phenomenology and interpreted as black holes of JT gravity. † e-mail: [email protected]; [email protected] * e-mail: [email protected]