Propagation of solitary waves in channels of decreasing depth

The changes which occur in a right-going solitary wave as it travels a channel of decreasing depth are discussed. In addition to the changes in the solitary wave, we have found through a judicious use of the conservation laws two secondary structures (a shelf and a reflection). Each of these structures is small with respect to the solitary wave, though the mass flux associated with each is of the same order as that of the solitary wave. Of interest is that the amplitude of the reflected wave does not satisfy Green's law. But rather, the amplitude of the reflected wave is constant along left-going characteristics. This finding allows us to satisfy the mass flux conservation laws to leading order and establishes the perturbed Korteweg-deVries equation as a consistent approximation for the right-going profile.