Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2401

Title: Spatial dynamics methods for solitary gravity-capillary water waves with an arbitrary distribution of vorticity
Authors: Groves, Mark D.
Wahlen, E.
Issue Date: 2006
Abstract: This paper presents existence theories for several families of small-amplitude solitarywave solutions to the classical water-wave problem in the presence of surface tension and with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram for irrotational solitary waves is shown to remain qualitatively unchanged for any choice of vorticity distribution. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial direction is the time-like variable. A centre-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite numer of degrees of freedom. Homoclinic solutions to the reduced system, which correspond to solitary water waves, are detected by a variety of dynamical systems methods.
Description: This is a pre-print
URI: https://dspace.lboro.ac.uk/2134/2401
Appears in Collections:Pre-prints (Maths)

Files associated with this item:

File Description SizeFormat
06-26.pdf340.89 kBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.