Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials.

We derive analytical solutions to the cubic-quintic nonlinear Schrödinger equation with potentials and nonlinearities depending on both propagation distance and transverse space. Among other, circle solitons and multi-peaked vortex solitons are found. These solitary waves propagate self-similarly and are characterized by three parameters, the modal numbers m and n, and the modulation depth of intensity.