Accurate computations for steep solitary waves

Abstract

Finite-amplitude solitary waves in water of arbitrary uniform depth are considered. A numerical scheme based on series truncation is presented to calculate the highest solitary wave. It is found that the ratio of the amplitude of the wave versus the depth is 0.83322. This value is compared with the values obtained by previous investigators. In addition, another numerical scheme based on an integral-equation formulation is derived to compute solitary waves of arbitrary amplitude. These calculations confirm and extend the calculations of Byatt-Smith & Longuet-Higgins (1976) for very steep waves.