On Wiener functionals of order 2 associated with soliton solutions of the KdV equation

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Abstract

The eigenvalues and eigenvectors of the Hilbert-Schmidt operators corresponding to the Wiener functionals of order 2, which give a rise of soliton solutions of the KdV equation, are determined. Two explicit expressions of the stochastic oscillatory integral with such Wiener functional as phase function are given; one is of infinite product type and the other is of Lévy's formula type. As an application, the asymptotic behavior of the stochastic oscillatory integral will be discussed.

Original languageEnglish
Pages (from-to)212-229
Number of pages18
JournalJournal of Functional Analysis
Volume216
Issue number1
DOIs
Publication statusPublished - Nov 1 2004

All Science Journal Classification (ASJC) codes

  • Analysis

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