This peper studies the nonlinear wave theory in shallow water via the Hamiltonian structure. The principal is the surface wave evolution on water contained in uniform channels. The Ploper Hamiltonian appoximating sche...This peper studies the nonlinear wave theory in shallow water via the Hamiltonian structure. The principal is the surface wave evolution on water contained in uniform channels. The Ploper Hamiltonian appoximating scheme for the more general case of waves that undergo transverse variations in amplitude in the course of longitudinal propagations is constructed. Some solutions for channels with different cross-sections,especially,the rectangular cross-section, are presented to elucidate the main features of the approxiamting scheme for the problem of interest. The obtained results shows that the nonlinear approximation of wave evolution in channels depends not only on water depth but also on a parameter determined by the geometric shape Of the channel.展开更多
文摘This peper studies the nonlinear wave theory in shallow water via the Hamiltonian structure. The principal is the surface wave evolution on water contained in uniform channels. The Ploper Hamiltonian appoximating scheme for the more general case of waves that undergo transverse variations in amplitude in the course of longitudinal propagations is constructed. Some solutions for channels with different cross-sections,especially,the rectangular cross-section, are presented to elucidate the main features of the approxiamting scheme for the problem of interest. The obtained results shows that the nonlinear approximation of wave evolution in channels depends not only on water depth but also on a parameter determined by the geometric shape Of the channel.
