Abstract
The dispersion relations and the approximate solutions of solitary-wave type are derived for several depth-averaged and depth-integrated nonlinear dispersive long wave equations. Solutions of depth-averaged equations for solitary wave tend to provide steep wave profile with narrow-width and high-wave hight compared with KdV solution. On the other hand, solutions of depth-integrated equations for solitary wave provide wide wave profile with wide-width and low-bight. On wave deformation and disintegration to the solitons, the difference is quite important. Not only theoretical examinations but also laboratory and numerical experiments show that depth-integrated Peregrine equation and Madsen & Sørensen equation are suitable for numerical analysis of tsunami.
