On Wiener functionals of order 2 associated with soliton solutions of the KdV equation
On Wiener functionals of order 2 associated with soliton solutions of the KdV equation
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DOI：
10.1016/j.jfa.2003.11.002
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发表时间：
2004-11
影响因子：
1.7
通讯作者：
S. Taniguchi
中科院分区：
文献类型：
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作者：
S. Taniguchi
确定了2阶Wiener泛函对应的Hilbert-Schmidt算子的本征值和本征向量，并给出了KdV方程孤子解的上升。给出了以相函数为Wiener泛函的随机振荡积分的两个显式表达式；一种是无限积型，另一种是lsamvy公式型。作为一个应用，我们将讨论随机振荡积分的渐近性质。
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.