It is possible to approach non-linear optics from the point of view of field theory. The central problem then is the interaction of non-linearity and dispersion. A simple example of this phenomenon is furnished by Boussinesq’s equation in hydraulics. In this paper the derivation and the range of validity of this equation are discussed. It is shown that the equation can be reduced to one of a simpler type. Some properties of this reduced equation are given.
Broer, L. J. F. (1964). On the interaction of non-linearity and dispersion in wave propagation : I. Boussinesq's equation. Applied Scientific Research, Section B, 11(3-4), 273-285. https://doi.org/10.1007/BF02922007