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Lectures on Nonlinear Wave Propagation

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Wave Propagation

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 81))

Abstract

The physical concept of a wave is a very general one. It includes the cases of a clearly identifiable disturbance, that may either be localised or non-localised, and which propagates in space with increasing time, a time-dependent disturbance throughout space that may or may not be repetitive in nature and which frequently has no persistent geometrical feature that can be said to propagate, and even periodic behaviour in space that is independent of the time. The most important single feature that characterises a wave when time is involved, and which separates wave-like behaviour from the mere dependence of a solution on time, is that some attribute of it can be shown to propagate in space at a finite speed.

In time dependent situations, the partial differential equations most closely associated with wave propagation are of hyperbolic type, and they may be either linear or nonlinear. However, when parabolic equations are considered whicji have nonlinear terms, then they also can often be regarded as describing wave propagation in the above-mentioned general sense. Their role in the study of nonlinear wave propagation is becoming increasingly important, and knowledge of the properties of their solutions, both qualitative and quantitative, is of considerable value when applications to physical problems are to be made. These equations frequently arise as a result of the determination of the asymptotic behaviour of a complicated system.

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Authors and Affiliations

  1. Department of Engineering Mathematics, The University Newcastle upon Tyne, NE1 7RU, England

    A. Jeffrey

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  1. A. Jeffrey
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Giorgio Ferrarese

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Jeffrey, A. (2010). Lectures on Nonlinear Wave Propagation. In: Ferrarese, G. (eds) Wave Propagation. C.I.M.E. Summer Schools, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11066-5_1

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