THE SOLITARY WAVES IN TROUGH EXCITED BY TWO FREQUENCY MODES
二模振荡激励下水槽中的孤立波

In a long and narrow trough parametrically excited by two frequency modes along vertical direction, the irrotational movement of an incompressible inviscid fluid has been investigated. Using the methods of multi-scale and average variational principle a nonlinear partial differential equations have been derived, that the complex displacement of the movement of fluid surface must satisfy. Under certain conditions, the solution of that equation can be obtained, it's a solitary wave with the waveform as hyperbolic secant function. Correspondingly the relations between the water parameters and the exciting variables have been discussed.