|TITLE||An Introduction to Inverse Scattering Transform|
It is an introductory talk on inverse scattering transform method in integrable systems. The inverse scattering transform (IST) is a method for solving some non-linear partial differential equations. The method is a non-linear analogue of the Fourier transform. This method was first introduced by Gardner-Greene-Kruskal-Miura for the Korteweg–de Vries equation, and soon extended to the nonlinear Schrodinger equation, sine-Gordon equation, the Toda lattice equation and so on. In this talk, I will introduce the IST for Kdv and Toda Lattice, and the connection between IST and Riemann-Hilbert problem.