Soliton Theory and Hankel Operators
Soliton Theory and Hankel Operators
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孤子理论和汉克尔算子
DOI：
10.1137/151004926
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. Rybkin
中科院分区：
文献类型：
--
作者：
S. Grudsky;A. Rybkin
孤立子理论和汉克尔（和托普利茨）算子理论基本上是相互封闭的。本文所关注的是将这两个非常活跃和非常庞大的理论联系起来。在Korteweg-de弗里斯（KdV）方程柯西问题的典型示例中，我们证明了汉克尔算子语言的力量，其中符号可以方便地用与KdV方程初始数据相关的薛定谔算子的散射数据来表示。这种方法产生捷径已经知道的结果，以及各种新的（例如，超出标准假设的初始数据的适定性），这是通过采用一些微妙的结果汉克尔算子。
Soliton theory and the theory of Hankel (and Toeplitz) operators have stayed essentially hermetic to each other. This paper is concerned with linking together these two very active and extremely large theories. On the prototypical example of the Cauchy problem for the Korteweg-de Vries (KdV) equation we demonstrate the power of the language of Hankel operators in which symbols are conveniently represented in terms of the scattering data for the Schrodinger operator associated with the initial data for the KdV equation. This approach yields short-cuts to already known results as well as to a variety of new ones (e.g. wellposedness beyond standard assumptions on the initial data) which are achieved by employing some subtle results for Hankel operators.