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

Content Provider	Springer Nature Link
Author	Dobrokhotov, S. Yu. Minenkov, D. S. Rouleux, M.
Copyright Year	2015
Abstract	We consider two-dimensional asymptotic formulas based on the Maslov canonical operator arising in stationary problems for differential and pseudodifferential equations. In the case of Lagrangian manifolds invariant with respect to Hamiltonian flow with Hamiltonians of the form F(x, \|p\|), we show how asymptotic formulas can be simplified by using the well-known (in classical mechanics) Maupertuis-Jacobi correspondence principle to replace the Hamiltonians F(x, \|p\|) by Hamiltonians of the form C(x)\|p\| arising, in particular, in geometric optics and related to the Finsler metric. As examples, we consider Hamiltonians corresponding to the Schrödinger equation, the two-dimensional Dirac equation, and the pseudodifferential equations for surface water waves.
Starting Page	42
Ending Page	49
Page Count	8
File Format	PDF
ISSN	00014346
Journal	Mathematical Notes
Volume Number	97
Issue Number	1-2
e-ISSN	15738876
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-03-01
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Maupertuis-Jacobi correspondence principle Lagrangian manifold Maslov canonical operator Hamiltonian Schrödinger equation Dirac equation Hamiltonian flow surface water wave pseudodifferential equation Mathematics
Content Type	Text
Resource Type	Article

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