Shock-like Waves with Finite Amplitudes

The tidal wave in the Qiantang River, Hangzhou City, China is quite different from that of the KdV equation, it is a shock-like wave with a finite amplitude. This phenomenon has mathematicians adjusting their solitary wave models on how such waves behave. This paper applies the variational theory to insight into the energy behavior of the tidal wave, which can be modeled by the Benny-Luke equation, and the exp-function method is used to figure out the solution structure. This paper provides a new window for designing energy-harvesting devices from the shock-like waves.