Ermakov-Ray-Reid systems in nonlinear optics

Colin Rogers*, Boris Malomed, Kwok Chow, Hongli An

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 twocomponent 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.

Original languageEnglish
Article number455214
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number45
DOIs
StatePublished - 12 Nov 2010

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