On the directly generated resonant standing waves in a rectangular tank

A numerical study based on the nonlinear Schrodinger equation, as applied to nonlinear resonant standing waves excited directly by a wavemaker in a rectangular tank, is presented. The stationary solutions of the problem serve as a starting point of the investigation. Bifurcations from a single steady state to multiple stationary solutions are obtained for several values of damping coefficients along the tank and at the wavemaker. The stability of the latter solutions is tested. Limit-cycle or fixed-point solutions are obtained. The results of the numerical study are discussed in connection with experimental data. The necessity of incorporation of dissipation at the wavemaker in the theoretical model in order to obtain qualitative agreement with experiment is demonstrated.