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Keywords
- Gedächtnis
- Nichtlineare Wellen
- inhomogene Medien
- inhomogeneous media
- memory effects
- nichtlineare Dynamik
- nonlinear dynamics
- nonlinear waves
- short wave processes
About this book
This booklet presents a study of one-dimensional waves in solids which can be modelled by nonlinear wave equations of different types. The factorization method is the main tool in this analysis. It allows for an exact or at least asymp totic decomposition of the wave(s) under consideration in terms of first order multipliers. Chapter 1 provides a general introduction. It presents some well-known results on characteristics, Riemann invariants, simple waves, etc. The main result of Chap. 1 is Theorem 1.3.2. (Sect. 1.3.2) which establishes the possibility of exact factorization of the nonlinear wave equation EPa(a) 1 EPa _ 0 Ij(l-u- x2 with constant coefficients. This theorem permits one to construct further factor izations of more complicated wave equations which the reader will meet in the following chapters. Chapter 2 is devoted to short wave processes in inhomogeneous media, the main result being the uniform asymptotic factorization of nonlinear wave equa tions with variable coefficients and the description of corresponding single-wave processes without the usual assumption of a small wave amplitude.
Bibliographic Information
Book Title: Nonlinear Waves in Inhomogeneous and Hereditary Media
Authors: Alexandr A. Lokshin, Elena A. Sagomonyan
Series Title: Research Reports in Physics
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1992
Softcover ISBN: 978-3-540-54536-1Published: 30 March 1992
Series ISSN: 0939-7426
Edition Number: 1
Number of Pages: X, 121
Number of Illustrations: 4 b/w illustrations