SDIFF(2) KP HIERARCHY
SDIFF(2) KP HIERARCHY
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DOI：
10.1142/s0217751x92004099
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发表时间：
1991-12
影响因子：
1.6
通讯作者：
K. Takasaki;T. Takebe
中科院分区：
文献类型：
--
作者：
K. Takasaki;T. Takebe
本文提出了KP族的一个类似物，SDiff（2）KP族，它与柱面上的保面积同态群有关。一个改进的Lax形式主义的KP层次结构给出了一个原型，这个新的层次结构。引入了两个重要的势S和τ。后者是普通KP层次结构的tau函数的对应物。一个与面积-代数同态群相关的Riemann-Hilbert问题给出了一般解的扭量理论描述（非线性引力构造）。在Riemann-Hilbert问题的框架下，确定了一个与拓扑极小模型相关的特殊解族。进一步构造了该族的无穷小对称。在tau函数的层次上，这些对称性服从反常的对易关系，因此导致了无穷小面积保持同态代数（或相关的泊松代数）的中心扩展。
An analogue of the KP hierarchy, the SDiff(2) KP hierarchy, related to the group of area-preserving diffeomorphisms on a cylinder is proposed. An improved Lax formalism of the KP hierarchy is shown to give a prototype of this new hierarchy. Two important potentials, S and τ, are introduced. The latter is a counterpart of the tau function of the ordinary KP hierarchy. A Riemann-Hilbert problem relative to the group of area-diffeomorphisms gives a twistor theoretical description (nonlinear gravition construction) of general solutions. A special family of solutions related to topological minimal models are identified in the framework of the Riemann-Hilbert problem. Further, infinitesimal symmetries of the hierarchy are constructed. At the level of the tau function, these symmetries obey anomalous commutation relations, hence leads to a central extension of the algebra of infinitesimal area-preserving diffeomorphisms (or of the associated Poisson algebra).