主讲人：聂兆虎 教授（犹他州立大学）

时  间：2014年6月11日（周三）11:00-12:00

地  点：必赢76net线路官网北一区文科楼 201 教室

摘  要：The Liouville equation is the nonlinear second order partial differential equation u_{xy} = -e^{2u}. It is related to surfaces of constant curvature, and Liouville found the general solution. Toda field theories are generalizations of the Liouville equation using general simple Lie algebras. These are a typical class of integrable systems. In this talk, we will concentrate on two aspects of Toda field theories. The first one is about characteristic integrals, that is, some differential polynomials (with respect to one variable) in the unknown functions whose derivative with respect to the other variable is zero. These are conserved quantities for the system. The second is about the explicit solutions to the Toda field theories in the above spirit of Liouville. Leznov's general solutions will be presented in the most explicit form using iterated integrals. Some work in progress on the PDE versions of the Toda systems with singular sources may also be mentioned.