Vortex solitons of the (3+1)-dimensional spatially modulated cubic–quintic nonlinear Schrödinger equation with the transverse modulation

Abstract

Vortex solitons in the spatially modulated cubic–quintic nonlinear media are governed by a (3+1)-dimensional cubic–quintic nonlinear Schrodinger equation with spatially modulated nonlinearity and transverse modulation. Via the variable separation principle with the similarity transformation, we derive two families of vortex soliton solutions in the spatially modulated cubic–quintic nonlinear media. For the disappearing and parabolic transverse modulation, vortex solitons with different configurations are constructed. The similar configurations of vortex solitons exist for the same value of $$l-k$$ with the topological charge k and degree number l. Moreover, the number of the inner layer structure of vortex solitons getting rid of the package covering layer is related to $$(n-1)/2+1$$ with the soliton order number n. For the disappearing transverse modulation, there exist phase azimuthal jumps around their cores of vortex solitons with $$2\pi $$ phase change in every jump, and any two jumps one after another realize the change in $$\pi $$ . For the parabolic transverse modulation, all phases of vortex soliton exist k-jump, and every jump realizes the change in $$2\pi /k$$ ; thus, k-jumps totally realize the azimuthal change in $$2\pi $$ around their cores.