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Gaussian ensembles for the non-linear Schrödinger and KdV equations.

Blower, Gordon (2001) Gaussian ensembles for the non-linear Schrödinger and KdV equations. Stochastics & Stochastics Reports, 71 (3-4). pp. 177-200. ISSN 1470-1243

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Abstract

Let be the soliton solution to the nonlinear Schrdinger equation on the line. Following the approach of Lebowitz et al. (J. Statist. Phys. 54, 17-56 (1989)) to the periodic case, a family of Gaussian ensembles is introduced. This approximates the Gibbs measure in the sense that it is concentrated on locally bounded functions which are locally uniformly close to the soliton solution. The measure may be normalized when the inverse temperature is sufficiently small. The covariance matrix of the Gaussian process satisfies the Schrdinger equation obtained by linearizing the original equation about the soliton solution. Further, the Gaussian process is stationary with respect to time-shift and spatial translation, in Levitan's sense. Gaussian ensembles for the modified KdV equation are also introduced

Item Type: Article
Journal or Publication Title: Stochastics & Stochastics Reports
Uncontrolled Keywords: Gibbs measure ; Stationary stochastic process ; Nonlinear Schrodinger equation
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19297
Deposited By: ep_ss_importer
Deposited On: 18 Nov 2008 16:08
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 13:12
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19297

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