Normal form coordinates for the KdV equation having expansions in terms of pseudo-differential operators
speaker: Riccardo Montalto (Università degli Studi di Milano)abstract: Near an arbitrary compact family of finite dimensional tori, left invariant under the KdV flow, we construct a real analytic, ’normal form transformation’ for the KdV equation having the following main properties: (1) When restricted to the family of finite dimensional tori, the transformation coincides with the Birkhoff map. (2) Up to a remainder term, which is smoothing to any given order, it is a pseudo-differential operator of order 0 in the normal directions with principal part given by the Fourier transform. (3) It is canonical and the pullback of the KdV Hamiltonian is a paradifferential operator which is in normal form up to order three.
Such coordinates are a key ingredient for studying the stability of finite gap solutions of arbitrary size (periodic multisolitons) of the KdV equation under small, quasi-linear perturbations. This is a joint work with Thomas Kappeler.
timetable:
Tue 21 May, 15:50 - 16:40, Aula Dini
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