Resonance NLS Solitons as Black Holes in Madelung Fluid

TL;DR

This paper introduces a resonance version of the nonlinear Schrödinger equation linked to gravity models, where soliton solutions mimic black holes in a Madelung fluid, revealing new insights into wave dynamics and spacetime analogies.

Contribution

It presents a novel resonance NLS equation embedded in a reaction-diffusion system, connecting soliton solutions to AdS black holes and gravitational models.

Findings

Resonance NLS equation models black hole analogs.

Soliton solutions correspond to event horizons.

Collision-induced resonance states have specific lifetimes.

Abstract

A new resonance version of NLS equation is found and embedded to the reaction-diffusion 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.