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

DOI10.1111/j.1467-9590.2012.00557.xzbMath1280.35142OpenAlexW1602241171MaRDI QIDQ4906053

Colin Rogers, Hong-Li An, Boris A. Malomed

Publication date: 21 February 2013

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9590.2012.00557.x

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum equilibrium statistical mechanics (general) (82B10) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (22)

Multi-component Ermakov and non-autonomous many-body system connections ⋮ On a canonical nine-body problem. Integrable Ermakov decomposition via reciprocal transformations ⋮ A Novel Ermakov-Painlevé II System: N+1-Dimensional Coupled NLS and Elastodynamic Reductions ⋮ On Madelung systems in nonlinear optics: A reciprocal invariance ⋮ On Ermakov-Painlevé II systems. Integrable reduction ⋮ On \(q\)-Gaussian integrable Hamiltonian reductions in anisentropic magneto-gasdynamics ⋮ Reciprocal gausson phenomena in a Korteweg capillarity system ⋮ On a Novel Resonant Ermakov-NLS System: Painlevé Reduction ⋮ q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics ⋮ On integrable Ermakov-Painlevé IV systems ⋮ On a Coupled Nonlinear Schrödinger System: A Ermakov Connection ⋮ On a Ermakov-Painlevé II reduction in three-ion electrodiffusion. A Dirichlet boundary value problem ⋮ Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation ⋮ On Multi-component Ermakov Systems in a Two-Layer Fluid: Integrable Hamiltonian Structures and Exact Vortex Solutions ⋮ On modulated multi-component NLS systems: Ermakov invariants and integrable symmetry reduction ⋮ Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation ⋮ Hybrid Ermakov-Painlevé IV Systems ⋮ Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction ⋮ On Hybrid Ermakov-Painlevé Systems. Integrable Reduction ⋮ On Modulated NLS-Ermakov Systems ⋮ Localized and periodic wave patterns for a nonic nonlinear Schrödinger equation ⋮ On Dirichlet two-point boundary value problems for the Ermakov-Painlevé IV equation

Cites Work

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• On a (2+1)-dimensional Madelung system with logarithmic and with Bohm quantum potentials: Ermakov reduction

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