Geodesic
Dynamic Systems Admitting the Normal Shift and Wave Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 244-260
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We consider wave equations on Riemannian manifolds and investigate wave front dynamics in the semiclassical approximation. The problem of finding wave equations whose wave front dynamics is described by Newtonian dynamic systems admitting the normal shift is solved. A subclass of these dynamic systems that can be defined by modified Lagrange and Hamilton equations is described explicitly. 
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R. A. Sharipov. Dynamic Systems Admitting the Normal Shift and Wave Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 244-260. http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a6/

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