Ray theories for hyperbolic waves, Kinematical conservation laws (KCL) and applications

Prasad, Phoolan (2007) Ray theories for hyperbolic waves, Kinematical conservation laws (KCL) and applications Indian Journal of Pure and Applied Mathematics, 38 (5). pp. 467-490. ISSN 0019-5588

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Abstract

Ray theory, for the construction of the successive positions of a wavefront governed by linear hyperbolic equations, is a method which had its origin from the work of Fermat (and is related to Huygen's method). However, for a nonlinear wavefront governed by a hyperbolic system of quasilinear equations, the ray equations are coupled to a transport equation for an amplitude of the intensity of the wave on the wavefront and some progress has been made by us in its derivation and use. We have also derived some purely differential geometric results on a moving curve in a plane (surface ∊IR3), these kinematical conservation laws are intimately related to the ray theory. In this article, we review these recent results, derive same new results and highlight their applications, specially to a challenging problem: sonic boom produced by a maneuvering aerofoil.

Item Type:Article
Source:Copyright of this article belongs to Indian National Science Academy.
Keywords:Ray Theory; Kinematical Conservation Laws; Nonlinear Waves; Conservation Laws; Shock Propagation; Curved Shock; Bicharacteristic Lemma; Shock Dynamics; Sonic Boom; Cauchy Problem; Hyperbolic and Elliptic Systems; Fermat's Principle
ID Code:90369
Deposited On:09 May 2012 14:09
Last Modified:19 May 2016 04:36

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