Abstract
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 Schrödinger 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 Pöschl–Teller 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.
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