A study of the boussinesq equation as a wave propagation in shallow water

摘要

Shallow water waves has been expressed as a couple of equations by Whitham (1967). amny researchers have continued studies in this field by deriving the so-called Boussinesq equations. A straight forward derivation from the Whitham' shallow water equestions shall immediately produced a coupled form of Boussinesq equations. In this paper we use the Lagrange coordinates in order to derive the single Boussinesq equation to represent wave motion on the surface of shallow water. We shall also discuss its solution by using the Hirota bilinear method and the KP hierarchy of equestions.