Normal Form Coordinates for the KdV Equation Having Expansions in Terms of Pseudodifferential Operators
Articolo
Data di Pubblicazione:
2019
Citazione:
Normal Form Coordinates for the KdV Equation Having Expansions in Terms of Pseudodifferential Operators / T. Kappeler, R. Montalto. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - (2019). [Epub ahead of print] [10.1007/s00220-019-03498-1]
Abstract:
Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the KdV equation on the torus having the following two main properties: (1) up to a remainder term, which is smoothing to any given order, the coordinate transformation is a pseudodifferential operator of order 0 with principal part given by the Fourier transform and (2) the pullback of the KdV Hamiltonian is in normal form
up to order three and the corresponding Hamiltonian vector field admits an expansion in terms of a paradifferential operator. Such coordinates are a key ingredient for studying the stability of finite gap solutions of the KdV equation under small, quasi-linear
perturbations.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
T. Kappeler, R. Montalto
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