We will focus on the derivation of different model equations as approximations to the full water wave problem taking into account the Coriolis effect, the stratification and the vorticity. The derivation relies on an interplay of variational methods in the Lagrangian or the Hamiltonian formalism and small-parameter expansions. Integrable model equations, as weakly nonlinear approximations under various assumptions for the scale parameters, will be developed. The advantage of the integrable model equations is that they have very rich mathematical structures. The inverse scattering method will be applied to get analytic soliton solutions. By obtaining explicit multi-soliton solutions, we will reveal the wave-interactions as well as the propagation of wave packages for the obtained models, in the context of their geophysical relevance.
Research Team: Delia Ionescu-Kruse (Simon Stoilow Institute, Bucharest), Rossen I. Ivanov (TU Dublin)
Original Dates: June 29, 2020 - July 29, 2020 (postponed to 2022 due to COVID-19)