Some nonlinear problems of water waves in a channel

On the basis of some approximate equations derived for nonlinear water waves in a channel of variable cross section, several problems of interest, which have attracted much attention recently, will be taken up in this report. First, the authors consider the breaking of an acceleration wave moving toward a shoreline in a general channel. Next, the so-called infinite mass dilemma, which arises in the study of the development of a solitary wave in a channel of variable cross section, will be resolved. Finally, they shall use an approximation method to study the fission of solitons in a general channel and justify it.