### 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

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

## Cite this

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*354*(1707), 575-607. https://doi.org/10.1098/rsta.1996.0020