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甬江数学讲坛(2019年第8讲)

2019-05-20

报告题目: Classical Differential Geometry and the Generalised Hodograph Method(II)


报告人:Maxim  Pavlov 俄罗斯科学院列别德夫物理研究所 教授

报告时间:20190417日(星期三)1400-1600

报告地点:阳明学院303

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.