Georgia Institute of Technology College of Sciences

Many conservative PDE models can be written in a Hamiltonian form. They include Euler equations in fluids, Vlasov models for plasmas and galaxies, ideal MHD for plasmas, Gross–Pitaevskii equation for superfluids and Bose-Einstein condensates, and various water wave models (KDV, BBM, KP, Boussinesq systems etc). I will describe some dynamical problems of these models, from a more unifying point of view by using their Hamiltonian forms. They include: stability/instability of coherent states (steady solution, traveling waves, standing waves etc.), invariant manifolds near unstable states, and inviscid and enhanced damping in fluids and plasmas. It is a topic course that will be taught in the fall.