Head on collision between capillary gravity solitary waves
The present study deals with the head on collision process between capillary gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu's Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincare Lighthill Kuo method. The resulting series solutions are given up to third order approximation. The physical features are discussed for wave speed, head on collision profile, maximum run up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary wave profile significantly. However, the maximum run up amplitude was affected in great measure due to the surface tension and the free parameter.