OVER A VARIABLE DEPTH

A theoretical study of water waves and current over variable depth is performed. Multiple-scalesanalysis is used to derive the equation governing the evolution of a 1-D wave packet. The current is assumed to be colinear with the wave number vector and with the depth gradient. The equation which is found is a cubic Schr6dinger equation with nonconstant coefficients. Some analytical properties of this equation are studied. The equation is then solved numerically and the effect of current and depth variation on the propagation of a solitary wave is studied