Particle dynamics in the KdV approximation

Abstract

The KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed numerically. The solutions treated here comprise the solitary wave, periodic traveling waves, and the two-soliton solutions. For solitary waves and periodic traveling waves, approximate particle paths are found in closed form.