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Normal form coordinates for the KdV equation near finite gap potentials

Riccardo Montalto
Univ. Zurich
Thursday, May 3, 2018 - 14:30

In this talk I will present the construction of real analytic, canonical coordinates for the KdV equation on the circle near an arbitrary finite gap potential (periodic multi-soliton) having the following two main properties: (1) these coordinates admit expansions in terms of pseudo-differential operators and (2) the KdV Hamiltonian vector field, when expressed in these coordinates, is in normal form up to order three.  Such coordinates are a key ingredient for studying the stability of finite gap solutions of the KdV equation under quasi-linear perturbations. This is a joint work with Thomas Kappeler

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