Tronquée solutions of the painlevé II equation
Tronquée solutions of the painlevé II equation
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painlevé II 方程的 Tronquee 解
DOI：
10.1007/s11232-012-0102-x
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发表时间：
2012
影响因子：
1
通讯作者：
V. Novokshenov
中科院分区：
文献类型：
--
作者：
V. Novokshenov
研究了painleveveii （PII）方程的特解，即复平面上沿一条或多条临界射线没有极点的特解。它们由Lax对方程的特殊单数据参数化。一般解的一元数据流形是一个具有一维和零维奇点的二维复流形，这是由于流形没有全局参数化而产生的。我们证明了这些且只有这些奇点（连同参数化的零点）与PII方程的tronque解有关。作为例证，我们考虑了已知的Hastings-McLeod解和Ablowitz-Segur解以及其他一些解，以证明它们属于tronquamee解的一类，并对应于单数据的一种或另一种奇点。
We study special solutions of the Painlevé II (PII) equation called tronquée solutions, i.e., those having no poles along one or more critical rays in the complex plane. They are parameterized by special monodromy data of the Lax pair equations. The manifold of the monodromy data for a general solution is a twodimensional complex manifold with one- and zero-dimensional singularities, which arise because there is no global parameterization of the manifold. We show that these and only these singularities (together with zeros of the parameterization) are related to the tronquée solutions of the PII equation. As an illustration, we consider the known Hastings-McLeod and Ablowitz-Segur solutions and some other solutions to show that they belong to the class of tronquée solutions and correspond to one or another type of singularity of the monodromy data.