Abstract
The talk presents, in short, the history of internal wave research, primarily the short waves in the world's oceans, an overview of a few main focuses of international internal wave research, and also, some new results on how internal waves become unstable and break. The breaking process is of fundamental importance to the energy cascade taking place in the ocean, and is a contribution to improved understanding to oceanography, but involves hydrodynamicists, applied mathematicians and experimentalists. A typical feature of the internal waves - internal solitons - is the large amplitude, sometimes as large as 4-5 times the level at rest. The nonlinear mathematics and experiments go beyond the inverse scattering theory and the integrable equations, and attains increased attention by theoretical mathematicians.