Elastic wavelets and their application to problems of solitary wave propagation
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| Title | Elastic wavelets and their application to problems of solitary wave propagation |
| Authors | |
| 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. |
| Publisher | Accademia Peloritana dei Pericolanti |
| Date | 2008-03-03 |
| Source | 0365-0359 |
| Rights | Articles and conference papers published in Atti della Accademia Peloritana dei Pericolanti – Classe di Scienze Fisiche, Matematiche e Naturali are distributed under the terms and conditions of a Creative Commons Attribution 3.0 Unported License (effective since 2009, Vol. 87). Correspondingly, authors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work´s authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal´s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access). |