Exact vector multipole and vortex solitons in the media with spatially modulated cubic–quintic nonlinearity

A (2+1)-dimensional N-coupled nonlinear Schrödinger equation with spatially modulated cubic–quintic nonlinearity and transverse modulation is studied, and vector multipole and vortex soliton solutions are analytically obtained. When the modulation depth q is chosen as 0 and 1, vector multipole and vortex solitons are constructed, respectively. The number of "petals" for the multipole solitons and vortex solitons is related to the value of the topological charge m, and the number of layers in the multipole solitons and vortex solitons is determined by the value of the soliton order number n.