Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
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DOI：
10.1007/s00029-016-0225-2
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
G. Genovese;R. Lucà;Daniele Valeri
中科院分区：
文献类型：
--
作者：
G. Genovese;R. Lucà;Daniele Valeri
研究一维周期导数非线性Schrödinger方程。我们知道这是一个完全可积的系统，在这个意义上，有一个无限的运动形式积分序列。在每一项中，具有最高正则性的项涉及到DNLS方程解的索博列夫范数。我们证明了一个函数测度，绝对连续的，带协方差的高斯测度，与运动的每个积分相关联。
We study the one-dimensional periodic derivative nonlinear Schrödinger equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion,. In eachthe term with the highest regularity involves the Sobolev normof the solution of the DNLS equation. We show that a functional measure on, absolutely continuous w.r.t. the Gaussian measure with covariance, is associated to each integral of motion,.