Strongly Nonlinear Wave Phenomena in the Ocean

In the ocean, it is common to observe strongly nonlinear wave phenomena for which any classical (weakly nonlinear) asymptotic models are no longer valid. In this talk I will propose new mathematical models to describe the evolution of these strongly nonlinear waves in both shallow and deep ocean. Solitary wave solutions of the new models will be compared with various experiments and field observations and effects of nonlinear dispersion often neglected in any weakly nonlinear models will be addressed. We will discuss some details of the stability and dynamics of interfacial waves in two-layer system and rotational waves in shallow water of uniform vorticity.