The theory of symmetrical gravity waves of finite amplitude II. The solitary wave

Abstract

Abstract An exact solution is obtained to a problem which differs from the two-dimensional problem of the solitary wave only in that the non-linear condition on the free surface is replaced by a slightly modified non-linear boundary condition having the same qualitative behaviour. Expressions are obtained for the wave velocity and amplitude, and also the equation of the free surface in parametric form. Breaking conditions at the crest are also investigated.