To the Theory of Generalized Burgers' Equations
Abstract:Connections are given between partial differential equations describing nonlinear acoustic waves propagating in one space dimension in a dissipative medium. Equations governing low-frequency waves in tubes with varying cross section, high-frequency wave propagation through inhomogeneous media, the behaviour of spherical and cylindrical waves, the amplification of travelling waves, etc., can be reduced to the form of a generalized Burgers' equation (GBE). Approaches which can be used for finding exact and approximate analytical results are described. Cases where exact self-similar solutions exist are considered. An alternative form of GBE, which offers additional possibilities of analytical studies of 1D nonlinear waves is derived. New self-similar solutions are found. Generalized Burgers' equations of special forms, corresponding, for example, to an exponential concentrator or to a wave amplified during the propagation along a nonuniformly heated plate, are solved by the method of matched asymptotic expansions.
Document Type: Research Article
Publication date: 2002-03-01
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- Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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