The Shape of Soliton-Like Solutions of a Higher-Order Kdv Equation Describing Water Waves

We study the solitary wave solutions of a non-integrable generalized KdV equation proposed by Fokas [A. S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional waves in shallow water with greater accuracy than standard equation. This includes higher-order terms small parameters α and β, representing respectively height inverse width compared thickness sheet. The we find have smaller larger corresponding soliton at same propagation velocity. Extrapolating these results conjecture that — limit arbitrarily high order β will attain specific, finite as speed c increases.