# Spatial solitons in thermo-optical media from the nonlinear Schrodinger-Poisson equation and dark matter analogues

## TL;DR

This paper studies the behavior of spatial solitons in thermo-optical media using a nonlinear Schrödinger-Poisson model, revealing analogies with dark matter phenomena and providing numerical solutions for various soliton states.

## Contribution

It introduces a theoretical analysis of the Schrödinger-Poisson equation with Kerr nonlinearity in two dimensions, including numerical solutions and dark matter analogies.

## Key findings

- Numerical family of radially symmetric ground state solutions.
- Analysis of excited states and oscillations.
- Simulations of soliton interactions resembling galactic core dynamics.

## Abstract

We analyze theoretically the Schrodinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermooptical media and can be regarded as an analogue system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark matter scenario.