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 Matem. Mod., 2013, Volume 25, Number 2, Pages 19–32 (Mi mm3328)

Simulation of wave front dynamics and metamorphoses of caustics

K. S. Arakelov

Moscow State University

Abstract: The dynamics of wave front, considered in ray limit, which propagates in the field of two equal repulsive Coulomb force centers, was simulated with the help of specially designed program tool. Correspondent task of evolution of point particle in this potential field was studied both in classical mechanics and semiclassical limit of quantum mechanics. The computer algorithm for caustics calculations was introduced. In the numeric experiments the Lagrange surfaces, corresponding to wave fronts, were obtained and their transformations were considered. It was shown that analysis of the Lagrange surfaces can be helpful for determination of correct parameters of numerical experiments in order to get fine structure of caustics. It was shown that the focusing of initially flat wave front takes place during evolution in potential considered. The ability of focusing was studied theoretically by investigation of system dynamics in elliptic coordinates. The density of caustic points was obtained. It was shown that this density depends on the types of singularity of correspondent wave fronts. The dependency between this density and phase shift of wave function of correspondent quantum task in semiclassical limit was demonstrated.

Keywords: wave fronts, caustics, metamorphoses, focusing, numerical experiments.

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Citation: K. S. Arakelov, “Simulation of wave front dynamics and metamorphoses of caustics”, Matem. Mod., 25:2 (2013), 19–32

Citation in format AMSBIB
\Bibitem{Ara13} \by K.~S.~Arakelov \paper Simulation of wave front dynamics and metamorphoses of caustics \jour Matem. Mod. \yr 2013 \vol 25 \issue 2 \pages 19--32 \mathnet{http://mi.mathnet.ru/mm3328} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3112310}