Browsing by Author "Valeri, Daniele"

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    Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2015) Genovese, Giuseppe; Lucà, Renato; Valeri, Daniele
    We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion R hk, k 2 Z+. In each R h2k the term with the highest regularity involves the Sobolev norm _H k(T) of the solution of the DNLS equation. We show that a functional measure on L2(T), absolutely continuous w.r.t. the Gaussian measure with covariance (I + ()k) 1, is associated to each integral of motion R h2k, k 1.