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

Setsuo Taniguchi

doi:10.1016/j.jfa.2003.11.002

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

Setsuo Taniguchi

Division for Theoretical Natural Science

Research output: Contribution to journal › Article

3 Citations (Scopus)

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 language	English
Pages (from-to)	212-229
Number of pages	18
Journal	Journal of Functional Analysis
Volume	216
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2003.11.002
Publication status	Published - Nov 1 2004

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2003.11.002

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Taniguchi, S. (2004). On Wiener functionals of order 2 associated with soliton solutions of the KdV equation. Journal of Functional Analysis, 216(1), 212-229. https://doi.org/10.1016/j.jfa.2003.11.002

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