Three-dimensional vector solitons and their stabilities in a Kerr medium with spatially inhomogeneous nonlinearity and transverse modulation

Analytical vector spatiotemporal soliton solutions are derived in a spatially inhomogeneous Kerr nonlinear medium with a transverse modulation by means of a generic transformation. As an example, spatiotemporal soliton clusters such as Gaussian soliton clusters and radially symmetric soliton clusters in the media with the parabolic transverse modulation and without transverse modulation are constructed. The stability of vector spatiotemporal soliton clusters is investigated analytically and numerically, and results indicate that in the spatially inhomogeneous Kerr nonlinear medium, besides the stable fundamental solitons, stable higher-order mode exists below the critical propagation constant.