The second approximation to cnoidal and solitary waves

摘要: The expansion method introduced by Friedrichs (1948) for the systematic development of shallow-water theory water waves large wavelength was used Keller to obtain first approximation finite-amplitude solitary wave Boussinesq (1872) and Rayleigh (1876), as well periodic permanent type, corresponding cnoidal Korteweg & de Vries (1895). present investigation extends Friedrich's so include terms up fourth order from a flat horizontal bottom, thereby obtains complete second approximations both waves. These show that, unlike approximation, vertical motions cannot be considered negligible, that pressure variation is no longer hydrostatic.