Ermakov–Ray–Reid Reductions of Variational Approximations in Nonlinear Optics

2012/07/13 by Colin Rogers, C. Rogers, Boris A. Malomed +2 · 4 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Advanced Fiber Laser Technologies

paper · doi:10.1111/j.1467-9590.2012.00557.x

Abstract

Integrable Hamiltonian systems of Ermakov‐Ray‐Reid type are shown to arise out of variational approximation to certain modulated NLS models as well as in spiralling elliptic soliton systems and their generalization in a Bose‐Einstein setting.

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• Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
• A discretisation of the Ermakov-Painlevé II equation: Dirichlet and Robin-type boundary value problems
• Whitham-Broer-Kaup Systems in Multi-dimensions: Quantum and Resonant NLS Connections

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