KAM Theory, PDE and Numerics – KEN

The aim of the KEN Project is the mathematical analysis of nonlinear time dependent differential systems stem from physical models, partial differential equations, finite dimensional systems and numerical schemes. The main idea is to blend together mathematicians coming from seemingly distant communities -Partial differential equations, dynamical systems and numerical analytists- around a common scientific idea, the notion of change of variables. This means construct normal form, preconditionners, specific transformations, diagonalisation, in order to simplify the systems and allow a simpler analysis or numerical treatment. The main equations considered are nonlinear transport equations arising in kinetic and fluid dynamics, dispersive wave and Schroedinger equations, discrete models (lattice dynamics and time integrators) and forced system (like KEEN waves in plasma physics). The main questions will be the analysis of rigorous stability results or description of weakly turbulent mechanisms. The tools used will be coming from PDEs, dynamical systems and discretized models analysis linked with efficient numerical simulations. All of them are based on the choice or good variables that can be explicit of constructible. This is the central point of this proposition.