title: Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials.
abstract: 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. We find that the stable fundamental solitons with m = 0 and the low-order solitons with m = 1, n ≤ 2 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.
authors.forename: Si-Liu
authors.initials: SL
authors.lastname: Xu
authors.forename: Jia-Xi
authors.initials: JX
authors.lastname: Cheng
authors.forename: Milivoj R
authors.initials: MR
authors.lastname: Belić
authors.forename: Zheng-Long
authors.initials: ZL
authors.lastname: Hu
authors.forename: Yuan
authors.initials: Y
authors.lastname: Zhao