Bulletin of the American Mathematical Society

Author(s): Adrian Constantin; Joachim Escher
Journal: Bull. Amer. Math. Soc. 44 (2007), 423-431.
MSC (2000): Primary 35J65, 35Q35, 34C05, 76B15
Posted: April 12, 2007
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Abstract: Analyzing a free boundary problem for harmonic functions in an infinite planar domain, we prove that in a solitary water wave each particle is transported in the wave direction but slower than the wave speed. As the solitary wave propagates, all particles located ahead of the wave crest are lifted, while those behind it experience a downward motion, with the particle trajectory having asymptotically the same height above the flat bed.

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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 35J65, 35Q35, 34C05, 76B15

Adrian Constantin
Affiliation: School of Mathematics, Trinity College Dublin, Dublin 2, Ireland; and Department of Mathematics, Lund University, 22100 Lund, Sweden
Email: adrian@maths.tcd.ie, adrian.constantin@math.lu.se

Joachim Escher
Affiliation: Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1 30167 Hannover, Germany
Email: escher@ifam.uni-hannover.de

DOI: 10.1090/S0273-0979-07-01159-7
PII: S 0273-0979(07)01159-7
Keywords: Solitary wave, potential flow, particle trajectory.
Received by editor(s): September 7, 2006
Posted: April 12, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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Ionescu-Kruse D, Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity , DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 19 (2007), 531-543.

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