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