An asymptotic derivation of weakly nonlinear ray theory

Prasad, Phoolan (2000) An asymptotic derivation of weakly nonlinear ray theory. In: Proceedings of the Indian Academy of Sciences Mathematical Sciences, 110 (4). pp. 431-447.

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Abstract

Using a method of expansion similar to Chapman-Enskog expansion, a new formal perturbation scheme based on high frequency approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears. The transport equation for the amplitude has been deduced with an error O(epsilon (2)) where epsilon is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet-Bruhats theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading order terms give the weakly nonlinear ray theory (WNLRT) of Prasad, which has been very successful in giving physically realistic results and also in showing that the caustic of a linear theory is resolved when nonlinear effects are included. The weak shock ray theory with infinite system of compatibility conditions also follows from this theory.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences Mathematical Sciences
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian Academy of Sciences
Keywords:	Nonlinear wave propagation;ray theory;hyperbolic equations;caustic
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	13 Sep 2004
Last Modified:	19 Sep 2010 04:16
URI:	http://eprints.iisc.ac.in/id/eprint/1806

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