Spatial solitons in nonlinear Schrödinger equation with variable nonlinearity and quadratic external potential

An improved self-similar transformation is used to construct exact solutions of the nonlinear Schrödinger equation with variable nonlinearity and quadratic external potential, which both depend on the distance of propagation and the transverse spatial coordinate. By means of analytical and numerical methods we reveal the main features of the spatial solitons found. We focus on the most important optical examples, where the applied optical field is a function of both linearly or periodically varying distance and spatial coordinate. In the case of periodically varying nonlinearity, the variations of confining external potential are found to be signreversible (periodically attractive and repulsive) and thus supporting the soliton management.