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.