报告题目： Classical Differential Geometry and the Generalised Hodograph Method
报告人：Maxim Pavlov 俄罗斯科学院列别德夫物理研究所 教授
报告摘要：We consider the concept of the differential-geometric Poisson brackets, which were introduced by B.A. Dubrovin and S.P. Novikov at 1983. These Dubrovin-Novikov brackets are determined by the homogeneous differential operators of first order. Every term of these Poisson brackets has a differential-geometric interpretation. We introduce such objects like: hydrodynamic type systems, hydrodynamic conservation laws, hydrodynamic commuting flows. Independently we consider a class of Ferapontov brackets generalising Dubrovin-Novikov brackets from local to nonlocal case. Also we present the Tsarev Generalised Hodograph Method. Consider the Hodograph Method, and Reciprocal Transformations (the Liouville correspondence in a particular case). We consider the "Lax pairs" for description of corresponding integrable systems, and discuss construction of particular solutions.