标题： 酉矩阵模型和 Painlevé III 显示英文标题

标题： Unitary Matrix Models and Painlevé III

摘要： 我们从可积方程和字符串方程的角度讨论了完整的幺正矩阵模型。通过耦合Toda方程和字符串方程，我们推导出了Painlevé III方程的一个特例。从Virasoro约束出发，我们可以使用径向坐标。$t_{1}$与$t_{-1}$之间的关系类似于复共轭。由此期望$t\bar{t}$拓扑sigma模型的融合。 显示英文摘要

摘要： We discussed the full unitary matrix models from the view points of integrable equations and string equations. Coupling the Toda equations and the string equations, we derive a special case of the Painlev\'{e} III equation. From the Virasoro constrains, we can use the radial coordinate. The relation between $t_{1}$ and $t_{-1}$ is like the complex conjugate. %An implicit to the $t\bar{t}$ fusion of topological sigma model %is therby expected.