A Simple Approach for Shallow-Water Solitary Wave Interactions

This paper presents analysis of the nonlinear interaction of a pair of solitary waves, the splitting of an isolated hump into a train of solitary waves, and the fission of a single solitary wave on reaching a shelf. Such interactions and splitting behaviour are usually described in the Korteweg–de Vries equation using the Hirota method, or more generally in terms of inverse scattering, a type of nonlinear Fourier transform theory. However, virtually identical results can be obtained using simple physical arguments based on a combination of mass, momentum and energy conservation, with linear scattering from the shelf edge for the shelf interaction. This approximate approach can also be applied to other hydrodynamic equations such as the regularised long wave or Peregrine equation for which inverse scattering methods are not possible.