Abstract

Applying the similarity transformation, we construct the exact vortex solutions for topological charge S ≥ 1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S ≥ 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.

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