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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)


Particle trajectories in solitary water waves

Authors: Adrian Constantin and Joachim Escher
Journal: Bull. Amer. Math. Soc. 44 (2007), 423-431
MSC (2000): Primary 35J65, 35Q35, 34C05, 76B15
Published electronically: April 12, 2007
MathSciNet review: 2318158
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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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Additional Information

Adrian Constantin
Affiliation: School of Mathematics, Trinity College Dublin, Dublin 2, Ireland; and Department of Mathematics, Lund University, 22100 Lund, Sweden

Joachim Escher
Affiliation: Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1 30167 Hannover, Germany

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

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