Capillary–gravity waves of solitary type on deep water

On physical grounds it was recently suggested that limiting capillary–gravity waves of solitary type may exist on the surface of deep water (Longuet-Higgins 1988). This paper describes accurate numerical calculations which support the conjecture. The limiting wave has a phase speed c = 0.9267 ( g τ) ¼ . It is one of a family of solitary waves having speeds c [les ] 1.30 ( g τ) ¼ . The maximum angle of inclination α max of the free surface is a monotonically decreasing function of the speed c . Physical arguments suggest that α max has a positive lower bound.