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Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity

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Author

Summary, in English

This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of the water-wave problem are respectively a solitary wave of elevation and a family of Stokes waves. (c) 2008 Elsevier B.V. All rights reserved.

Department/s

Publishing year

2008

Language

English

Pages

1530-1538

Publication/Series

Physica D: Nonlinear Phenomena

Volume

237

Issue

10-12

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • bifurcation theory
  • water waves
  • vorticity

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0167-2789