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Chueh-Hsin Chang

2014-02-12
09:30:00 - 11:30:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

The six Painleve equations (PI–PVI) were first discovered around the beginning of the twentieth century by Painleve, Gambier and their colleagues in an investigation of nonlinear second-order ordinary differential equations. Recently there has been considerable interest in the Painleve equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering. Consequently the Painleve equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations, despite being nonlinear equations. In this talk, we will review the remarkable properties of the Painleve equations, for example, Inverse problems for the Painleve equations, Hamiltonian structure and Backlund transformations.