Nonlinear interaction of long waves in shallow water

A nonlinear generation of harmonics due to nonlinearity in a long wave propaiating in shallow water has been considered. The Boussinesq equations taking into account friction against the bottom are solved by the asymptotic averaging method. A set of reduced equations was obtained for the amplitudes of nonlinearly interacting harmonics in a long wave depending on the distance from the coast. The set was solved by the Runge-Kutta method, and the results compared with the data of the specially designed laboratory experiment. The agreement of the calculated and observed amplitudes of the harmonics and of the fundamental wave is good. The conclusion is drawn that friction against the bottom plays an important role in the norilinear dynamics of long waves.