Boussinesq solution for solitary waves in uniform channels with sloping side walls

The analytical solution to the Boussinesq equations for solitary waves trav elling in uniform water channels with sloping side walls is presented. Quan titative effects of channel cross-sectional geometry and channel side-wall slope at the waterline on the wave profile and wave speed, as well as the c riteria for positive solitary waves to exist, are discussed. The new Boussi nesq solution is also compared with the existing Korteweg-de Vries solution obtained by Peregrine. It is found that the two solutions are consistent f or small amplitude waves while, for relatively large waves, the Boussinesq solution gives different predictions for wave speed and for the criteria fo r solitary waves to exist.