Variational approach to orthogonally-polarized optical soliton interactionwith cubic and quintic nonlinearities

A reduced variational technique is developed to describe the interaction of opposite-handed, circularly-polarized, d-dimensional solitons propagating in an isotropic material with both cubic and quintic nonlinearities. Dynami cal equations for the simultaneous collapse and interaction of the two soli tons are developed and are shown to be analogous to a particle in a (d + 2) -dimensional. potential well. This potential simultaneously describes the d ynamics of the interaction as well as the self- and cross-focusing of the t wo solitons. Stability and escape velocity formulas are derived and compare d to analytic and numerical results. The possibility of a "slingshot" inter action is revealed, even for d = 1 dimensional solitons, and its dynamics a re illustrated by direct integration of the variational state equations.