The Maupertuis-Jacobi principle for Hamiltonians of the form \(F(x,|p|)\) in two-dimensional stationary semiclassical problems

DOI10.1134/S0001434615010058zbMath1360.37159WikidataQ114075422 ScholiaQ114075422MaRDI QIDQ2353710

S. Yu. Dobrokhotov, D. S. Minenkov, Michel Rouleux

Publication date: 16 July 2015

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationDirac equationLagrangian manifoldMaslov canonical operatorpseudodifferential equationMaupertuis-Jacobi correspondence principlesurface water wave

Mathematics Subject Classification ID

Related Items (8)

Gaussian packets and beams with focal points in vector problems of plasma physics ⋮ Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain ⋮ The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides ⋮ Asymptotics of the Helmholtz equation solutions in a two-layer medium with a localized right-hand side ⋮ Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics ⋮ Electronic optics in graphene in the semiclassical approximation ⋮ Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side ⋮ Constructive semiclassical asymptotics of bound states of graphene in a constant magnetic field with small mass

Cites Work

• New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics
• Asymptotic expansions and the Maslov canonical opeator in the linear theory of water waves. I: Main constructions and equations for surface gravity waves
• Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations
• The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
• The Maupertuis Principle and Canonical Transformations of the Extended Phase Space
• Sobolev Spaces in Mathematics III
• ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
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