Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrdinger equation with spatially modulated nonlinearities and potentials.
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We derive analytical solutions to the cubic-quintic nonlinear Schrdinger 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. We find that the stable fundamental solitons with m = 0 and the low-order solitons with m = 1, n2 can be supported with the energy eigenvalues E = 0 and E 0. However, higher-order solitons display unstable propagation over prolonged distances. The stability of solutions is examined by numerical simulations.