Spatiotemporal vector and scalar solitons of the coupled nonlinear Schrödinger equation with spatially modulated cubic–quintic–septimal nonlinearities

The spatially modulated cubic–quintic–septimal nonlinearities and transverse modulation are introduced to study the impact on a (3 + 1)-dimensional N -coupled nonlinear Schrödinger equation. As an example, we derive two-component spatiotemporal localized mode solutions including vector multipole and vortex solitons and scalar soliton. The values of the modulation depth q and the topological charge k adjust the construction of vector and scalar solitons. If their values are both chosen as 0, scalar soliton is exhibited; if the value of the modulation depth q becomes 0 and 1, vector multipole and vortex solitons can be displayed, respectively. In two kinds of cubic–quintic–septimal nonlinear media with the transverse parabolic modulation and without transverse modulation, characteristics of vector multipole and vortex solitons and scalar soliton are discussed.