标题： 无色散Toda层次的旧和新约简 显示英文标题

标题： Old and New Reductions of Dispersionless Toda Hierarchy

摘要： 本文专注于色散无级Toda层次中两种特殊类型有限变量约化的几何方面。 这些约化是用“Landau-Ginzburg势”来表述的，这些势起到了约化Lax函数的作用。 其中一个是Dubrovin和Zhang的三角多项式的推广。 另一个是一个超越函数，其对数类似于色散无级KP层次的水袋模型。 它们都满足Löwner方程的径向版本。 这些Löwner方程的一致性产生了一个径向版本的Gibbons-Tsarev方程。 这些方程被用来制定约化层次的hodograph解。 Gibbons-Tsarev方程的几何方面用经典微分几何的语言（Darboux方程、Egorov度量和Combescure变换）进行解释。 给出了底层Egorov度量的平坦坐标。 显示英文摘要

摘要： This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of "Landau-Ginzburg potentials" that play the role of reduced Lax functions. One of them is a generalization of Dubrovin and Zhang's trigonometric polynomial. The other is a transcendental function, the logarithm of which resembles the waterbag models of the dispersionless KP hierarchy. They both satisfy a radial version of the L\"owner equations. Consistency of these L\"owner equations yields a radial version of the Gibbons-Tsarev equations. These equations are used to formulate hodograph solutions of the reduced hierarchy. Geometric aspects of the Gibbons-Tsarev equations are explained in the language of classical differential geometry (Darboux equations, Egorov metrics and Combescure transformations). Flat coordinates of the underlying Egorov metrics are presented.