Abstract
This paper considers the existence of solitary-wave solutions of the classical water-wave problem in the presence of surface tension. A region of Bond number-Proude number parameter space close to (1/3, 1) is identified, at each point of which there are infinitely many distinct multi-troughed solitary waves of depression. The method is to study a Hamiltonian formulation of the mathematical problem for solitary waves using a centre-manifold technique valid near Bond number 1/3 and Froude number 1. The problem is thus replaced by an equivalent problem posed on a four-dimensional manifold. In a certain region of parameter space near (1/3, 1), there is a Smale horseshoe in the dynamics on the centre manifold and therefore infinitely many distinct homoclinic orbits.
Original language | English |
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Pages (from-to) | 575-607 |
Number of pages | 33 |
Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 354 |
Issue number | 1707 |
DOIs | |
Publication status | Published - 15 Mar 1996 |
ASJC Scopus subject areas
- General Mathematics
- General Engineering
- General Physics and Astronomy