The Froude number for solitary waves

Abstract

SynopsisThe paper is concerned with the problem of a solitary wave moving with constant form and constant velocity c on the surface of an incompressible, inviscid fluid over a horizontal bottom. The motion is assumed to be two-dimensional and irrotational, and if h is the depth of the fluid at infinity and g the acceleration due to gravity, then the Froude number F is defined byThe result that F>1 has recently been proved by Amick and Toland by means of a long and complicated argument. Here we give a short and simple one.