Possible water wave solitons in a rectangular channel

A possible soliton state of water waves that can be excited in a rectangula r channel near cutoff frequency is presented. Using the hydrodynamic equati on and boundary conditions of water wave together with multiscale perturbat ion,the solvability condition corresponding to the governing equation for t he epsilon(3/2) order is obtained,which is a nonlinear Schrodinger equation in which lambda is a coefficient depending on the frequency difference bet ween the excited and cutoff frequencies. Ii the excited vibration moves as a sinusoidal oscillation, the lambda u term can be absorbed into the phase function. The coefficient K stands for the nonlinearity which critically de termines the character of the excited solitons,whether it is a bright or a dark soliton. When k(2)h < 1.022,it is possible to excite a dark soliton. T he bright surface solitons have been observed experimentally in a trough.