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

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Abstract

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.

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Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)1530-1538
TidskriftPhysica D: Nonlinear Phenomena
Volym237
Utgåva nummer10-12
StatusPublished - 2008
PublikationskategoriForskning
Peer review utfördJa