Dynamic systems admitting normal shift and wave equations

DOI10.1023/A:1015424831734zbMATH Open1055.58014arXivmath/0108158OpenAlexW2021506121MaRDI QIDQ1417372

D. Massart

Publication date: 4 January 2004

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Abstract: High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton equations being special case for Newton's equations. In simplest cases (e. g. light propagation in isotropic non-homogeneous refracting media) the dynamics of points preserves orthogonality of wave front and rays. This property was generalized in the theory of dynamical systems admitting normal shift of hypersurfaces. In present paper inverse problem is studied, i. e. the problem of reconstructing wave equation corresponding wave front dynamics for which is described by Newtonian dynamical system admitting normal shift of hypersurfaces in Riemannian manifold.

Full work available at URL: https://arxiv.org/abs/math/0108158

zbMATH Keywords

Riemannian manifoldsHamilton-Jacobi equations.wave front dynamics

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Hyperbolic equations on manifolds (58J45)

Related Items (2)

Multidimensional dynamical systems that admit normal shift ⋮ Dynamical systems that admit normal displacement

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