Nonlinear Wave Equations for Oceanic Internal Solitary Waves

In the coastal ocean, the interaction of barotropic tidal currents with topographic features such as the continental shelf, sills in narrow straits, and bottom ridges are often observed to generate large amplitude, horizontally propagating internal solitary waves. These are long nonlinear waves and hence can be modeled by equations of the Korteweg-de Vries type. Typically they occur in regions of variable bottom topography, with the consequence that the appropriate nonlinear evolution equation has variable coefficients. Further, as these waves can be long-lived it is necessary to take account of the effects of the Earth's background rotation. We review this family of model evolution equations and some of their pertinent solutions, obtained both asymptotically and numerically.