Vortex and multipole soliton modes in the (2+1)-dimensional cubic-quintic-septimal nonlinear media with the spatially modulated distributions

A (2 + 1)-dimensional cubic-quintic-septimal nonlinear Schrodinger equation with the spatially modulated distributions is investigated. When it is linked to the stationary cubic-quintic-septimal nonlinear Schrodinger equation, constraint conditions exist connecting inhomogeneous cubic, quintic and septimal nonlinearities and the amplitude of soliton mode. Under these conditions, analytical vortex and multipole soliton mode solutions are derived. If the value of the modulation depth is set as 1 and 0, vortex and multipole soliton modes are formed respectively. If the value of the soliton order number n grows, the layer structures of vortex and multipole soliton modes are added and are determined by the value of n. The stability of multipole and vortex soliton modes is tested by direct simulations with initial white noise.