An integral equation for unsteady surface waves and a comment on the Boussinesq equation

An integral equation for unsteady inviscid surface waves has been obtained. Existing known approximations are all derived from the one equation. The Boussinesq equation is obtained and criticized.

[1]  D. Peregrine.  Calculations of the development of an undular bore , 1966, Journal of Fluid Mechanics.

[2]  G. Whitham,et al.  Non-linear dispersive waves , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  G. Whitham.  A general approach to linear and non-linear dispersive waves using a Lagrangian , 1965, Journal of Fluid Mechanics.

[4]  E. Laitone,et al.  The second approximation to cnoidal and solitary waves , 1960, Journal of Fluid Mechanics.

[5]  D. Korteweg,et al.  XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[6]  L. C. Woods.  The theory of subsonic plane flow , 1961 .

[7]  G. B. Whitham,et al.  Variational methods and applications to water waves , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  P. Lax.  Integrals of Nonlinear Equations of Evolution and Solitary Waves , 1968 .