Elastic wavelets and their application to problems of solitary wave propagation

Rushchitsky, Jeremiah and Cattani, Carlo and Terletska, Katherina and Symchuk, Yaroslav (2008) Elastic wavelets and their application to problems of solitary wave propagation. Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze FF.MM.NN, LXXXVI (1). ISSN 1825-1242

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Abstract

The paper can be referred to that direction in the wavelet theory, which was called by Kaiser "the physical wavelets". He developed the analysis of first two kinds of physical wavelets - electromagnetic (optic) and acoustic wavelets. Newland developed the technique of application of harmonic wavelets especially for studying the harmonic vibrations. Recently Cattani and Rushchitsky proposed the 4th kind of physical wavelets - elastic wavelets. This proposal was based on three main elements: 1. Kaiser's idea of constructing the physical wavelets on the base of specially chosen (admissible) solutions of wave equations. 2. Developed by one of authors theory of solitary waves (with profiles in the form of Chebyshov-Hermite functions) propagated in elastic dispersive media. 3. The theory and practice of using the wavelet "Mexican Hat" system, the mother and farther wavelets (and their Fourier transforms) of which are analytically represented as the Chebyshov-Hermite functions of different indexes. An application of elastic wavelets to studying the evolution of solitary waves of different shape during their propagation through composite materials is shown on many examples.

Item Type:	Article
Subjects:	M.U.S. - Contributi Scientifici > 02 - Scienze fisiche M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali
Depositing User:	Mr Nunzio Femminò
Date Deposited:	03 Mar 2008
Last Modified:	13 Apr 2010 11:16
URI:	http://cab.unime.it/mus/id/eprint/475

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