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 | |
| Publication status | Published - Nov 1 2004 |
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All Science Journal Classification (ASJC) codes
- Analysis
Cite this
On Wiener functionals of order 2 associated with soliton solutions of the KdV equation. / Taniguchi, Setsuo.
In: Journal of Functional Analysis, Vol. 216, No. 1, 01.11.2004, p. 212-229.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On Wiener functionals of order 2 associated with soliton solutions of the KdV equation
AU - Taniguchi, Setsuo
PY - 2004/11/1
Y1 - 2004/11/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=4344679198&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2003.11.002
DO - 10.1016/j.jfa.2003.11.002
M3 - Article
AN - SCOPUS:4344679198
VL - 216
SP - 212
EP - 229
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -