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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 297, Pages 66–92
(Mi znsl1215)
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This article is cited in 8 scientific papers (total in 8 papers)
Gaussian beams, the Hamilton–Jacobi equations and Finsler geometry
A. P. Katchalov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
The relationships between Gaussian beams and geometry are considered in the paper. It is shown that the main properties of the Gaussian beam solutions are determined by the natural geometry, related to the problem under considerations. The geometry is determined by the Hamilton–Jacobi equation and corresponding hamiltonian. In particular, it was found a geometric interpretation of the Riccati equation for the quadratic form of the phase function corresponding to the Gaussian beam in the case of Finsler geometry.
Received: 25.01.2003
Citation:
A. P. Katchalov, “Gaussian beams, the Hamilton–Jacobi equations and Finsler geometry”, Mathematical problems in the theory of wave propagation. Part 32, Zap. Nauchn. Sem. POMI, 297, POMI, St. Petersburg, 2003, 66–92; J. Math. Sci. (N. Y.), 127:6 (2005), 2374–2388
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https://www.mathnet.ru/eng/znsl1215 https://www.mathnet.ru/eng/znsl/v297/p66
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Abstract page: | 561 | Full-text PDF : | 193 | References: | 71 |
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