Mathematical sciences seminar: Review of AKNS-ZS system in the set-up of Beals-Coifman - D-Bar method



Jyh-Hao Lee
Institute of Mathematics, Academia Sinica


This talk will be presented by two parts.We will review some results.


At first, we will review some old results about 2 by 2 AKNS system with linear and quadratic spectral parameter and the related evolution equations and the inverse scattering method under the set-up of Beals-Coifman. For the forward problem, we will explain the D-Bar idea to get the scattering data in this set-up, which is also applicable in higher dimensional cases. We will mention the ODE system for the direct problem in this set-up. This could be solved via the estimate of L1 norm and L2 norm of the potentials. Here the inverse problem is formulated as a Riemann-Hilbert problem.


Then we will make a brief introduction on the some recent papers based on this set-up . We will discuss some possible applications .