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

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.

13 pages, 11 figures

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• Single and merger soliton dynamics in scalar field dark matter with and without self-interactions
• Pressureless stationary solutions in a Newton-Yukawa gravity model
• Scaling of highly excited Schrödinger-Poisson eigenstates and universality of their rotation curves
• Tightly bound solitons and vortices in three-dimensional bosonic condensates with the electromagnetically-induced gravity
• Comparison of two different integration methods for the (1+1)-Dimensional Schrödinger-Poisson Equation
• Temporal dynamics of light-written waveguides in unbiased liquid crystals
• (1+1)-Dimensional Schrödinger-Poisson equation with contact interaction