On some solitary and cnoidal wave diffraction solutions of the Green-Naghdi equations

Nonlinear waves of the solitary and cnoidal types are studied in constant and variable water depths by use of the Irrotational Green-Naghdi (IGN) equations of different levels and the original Green-Naghdi (GN) equations (Level I). These equations, especially the IGN equations, have been established more recently than the classical water wave equations, therefore, only a handful applications of the equations are available. Moreover, their accuracies and the conditions under which they are applicable need to be studied. As a result, we consider a number of surface wave propagation and scattering problems that include soliton propagation and fission over a bump and onto a shelf, colliding solitons, soliton generation by an initial mound of water and diffraction of cnoidal waves due to a submerged bottom shelf, and compare the predictions with experimental data when available.