A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers

B. Buffoni, M. D. Groves, J. F. Toland

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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 languageEnglish
Pages (from-to)575-607
Number of pages33
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume354
Issue number1707
DOIs
Publication statusPublished - 15 Mar 1996

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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