On vortex and dark solitons in the cubic-quintic nonlinear Schrodinger equation

We study topologically charged propagation-invariant eigenstates of the 1+2-dimensional Schrodinger equation with a cubic (focusing)-quintic (defocusing) nonlinear term. First, we revisit the self-trapped vortex soliton solutions. Using a variational ansatz that allows us to describe the solutions as a liquid with a surface tension, we derive a simple formula relating the inner and outer radii of the bright vortex ring. Then, using numerical and variational techniques, we analyse dark soliton solutions for which the wave function density asymptotes to a non-vanishing value. We find an eigenvalue cutoff for the propagation constant that depends on the topological charge l. The variational profile provides simple and very accurate results for l >= 2. We also study the azimuthal stability of the eigenstates by a linear analysis finding that they are stable for all values of the propagation constant, at least for small l. (c) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

We investigate topologically charged propagation-invariant eigenstates of a 1+2-dimensional Schrodinger equation with a cubic-quintic nonlinear term. We derive a simple formula for the bright vortex ring's inner and outer radii and analyze dark soliton solutions, finding an eigenvalue cutoff dependent on the topological charge. Additionally, we study the azimuthal stability of the eigenstates and find they are stable for all propagation constants, at least for small topological charges.