Thomas Kappeler (University of Zurich)

On the wellposedness of integrable PDEs: a survey of new results for the KdV, KdV2, and mKdV equations

In form of a case study, I survey the ‘nonlinear Fourier‘ method to solve nonlinear dispersive equations such as the Korteweg-de Vries (KdV) equation or the nonlinear Schroedinger (NLS) equation. A key ingredient for desribing the solutions are the frequencies, associated to such type of equations. A novel approach of representing them allows to extend the solution map of such equations to spaces of low regularity and to study its regularity properties. Potential applications include results for stochastic versions of the evolution equations considered. This is joint work with Jan Molnar.