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Wave Motion: Theory, Modelling, and Computation
Volume 7 of the series Mathematical Sciences Research Institute Publications pp 295336
The Small Dispersion Limit of the KortewegDe Vries Equation
 Stephanos VenakidesAffiliated withStanford University
Abstract
There are many physical systems which display shocks i.e. regions in space where the solution develops extremely large slopes. In general, such systems are too complicated to be treated by exact calculation and their properties are best studied through the proof of general theorems. A model of the formation and propagation of dispersive shocks in one space dimension, in which explicit calculation is possible, is given by the initial value problem for the Kortewegde Vries equation:
in the limit ε → 0.
$$ {u_{t}}  6u{u_{x}} + {\varepsilon ^{2}}u{u_{{xxx}}} = 0 $$
(1.1a)
$$ u(x,o,\varepsilon ) =  v(x)$$
(1.1b)
 Title
 The Small Dispersion Limit of the KortewegDe Vries Equation
 Book Title
 Wave Motion: Theory, Modelling, and Computation
 Book Subtitle
 Proceedings of a Conference in Honor of the 60th Birthday of Peter D. Lax
 Pages
 pp 295336
 Copyright
 1987
 DOI
 10.1007/9781461395836_12
 Print ISBN
 9781461395850
 Online ISBN
 9781461395836
 Series Title
 Mathematical Sciences Research Institute Publications
 Series Volume
 7
 Series ISSN
 09404740
 Publisher
 Springer US
 Copyright Holder
 SpringerVerlag New York Inc.
 Additional Links
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 Editors

 Alexandre J. Chorin ^{(1)}
 Andrew J. Majda ^{(2)}
 Editor Affiliations

 1. Department of Mathematics, University of California
 2. Department of Mathematics, Princeton University
 Authors

 Stephanos Venakides ^{(3)}
 Author Affiliations

 3. Stanford University, USA
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