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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
