Paper

No solitary waves exist on 2D deep water

Published 23 October 2012 • © 2012 IOP Publishing Ltd & London Mathematical Society
, , Citation Vera Mikyoung Hur 2012 Nonlinearity 25 3301 DOI 10.1088/0951-7715/25/12/3301

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verahur@math.uiuc.edu

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1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Dates

  1. Received 19 February 2012
  2. Published

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0951-7715/25/12/3301

Abstract

The solitary wave problem at the free surface of a two-dimensional, infinitely-deep and irrotational flow of water under the influence of gravity is formulated as a nonlinear pseudodifferential equation. A Pohozaev identity is used to show that it admits no solutions which asymptotically vanish faster than linearly.

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10.1088/0951-7715/25/12/3301