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

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.