Ermakov-Ray-Reid systems in nonlinear optics

A hydrodynamics-type system incorporating a Madelung-Bohm-type quantum potential, as derived by Wagner et al via Maxwell's equations and the paraxial approximation in nonlinear optics, is reduced to a nonlinear Schrodinger canonical form. A two-parameter nonlinear Ermakov-Ray-Reid system that arises from this model, and which governs the evolution of beam radii in an elliptically polarised medium is shown to be reducible to a classical Posch-lTeller equation. A class of exact solutions to the Ermakov-type system is constructed in terms of elliptic dn functions. It is established that integrable two-component Ermakov-Ray-Reid subsystems likewise arise in a coupled (2+1)dimensional nonlinear optics model descriptive of the two-pulse interaction in a Kerr medium. The Hamiltonian structure of these subsystems allows their complete integration.