标题： 可积结构的色散系统与微分几何 显示英文标题

标题： Integrable structures of dispersionless systems and differential geometry

摘要： 我们发展了由流体动力学约化可积的Whitham型层理论，将其作为某种微分几何对象的理论。作为一个应用，我们构造了与任意亏格代数曲线模空间相关的Gibbons-Tsarev系统，并证明了通用Whitham层由流体动力学约化可积。 显示英文摘要

摘要： We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbons-Tsarev systems associated to moduli space of algebraic curves of arbitrary genus and prove that the universal Whitham hierarchy is integrable by hydrodynamic reductions.