论文标题
关于Bäcklund转换和Jordan概括的问题的问题
On the Question of the Bäcklund Transformations and Jordan Generalizations of the Second Painlevé Equation
论文作者
论文摘要
我们演示了从非线性Schrödinger方程（NLS）的变形中得出第二个Painlevé方程$ P_2 $及其Bäcklund变换的方法，同时一直保持严格的不变性相对于Schlesinger转换。所提出的算法允许构建基于$ P_2 $的Jordan代数完全可以集成的多场概括，同时还产生了相应的Bäcklund变换。我们建议将这样的模型称为JP系统。 For example, a Jordan algebra $J_{_{{\rm Mat}(N,N)}}$ with the Jordan product in the form of a semi-anticommutator is shown to generate an integrable matrix generalization of $P_2$, whereas the $V_{_N}$ algebra produces a different JP-system that serves as a generalization of the索科洛夫的矢量NLS形式。
We demonstrate the way to derive the second Painlevé equation $P_2$ and its Bäcklund transformations from the deformations of the Nonlinear Schrödinger equation (NLS), all the while preserving the strict invariance with respect to the Schlesinger transformations. The proposed algorithm allows for a construction of Jordan algebra-based completely integrable multiple-field generalizations of $P_2$ while also producing the corresponding Bäcklund transformations. We suggest calling such models the JP-systems. For example, a Jordan algebra $J_{_{{\rm Mat}(N,N)}}$ with the Jordan product in the form of a semi-anticommutator is shown to generate an integrable matrix generalization of $P_2$, whereas the $V_{_N}$ algebra produces a different JP-system that serves as a generalization of the Sokolov's form of a vectorial NLS.
