The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe a stationary moving wave patterns consisting of two plane solitary waves moving at an angle to each other. The results obtained within the approximate asymptotic theory is validated by comparison with the exact two-soliton solution of the Kadomtsev-Petviashvili equation.
The suggested approach is equally applicable to a wide class of non-integrable equations too. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin-Ono equation describing internal waves in the infinitely deep ocean containing a relatively thin one of the layers.
This video was produced by the Sydney Mathematical Research Institute, as part of their SMRI seminar series.
