Solvability of the derivative nonlinear Schr�dinger equation and the massive thirring model

Abstract

Here we review some results of J.-H. Lee of theN×N Zakharov-Shabat system with a polynomial spectral parameter. We define a scattering transform following the set-up of Beals-Coifman [2]. In the 2×2 cases, we modify the Kaup-Newell and Kuznetsov-Mikhailov system to assure the normalization with respect to the spectral parameter. Then we are able to apply the technique of Zakharov-Shabat for the solitons of NLS to our cases. We obtain the long-time behavior of the equations which can be transformed into DNLS and MTM in laboratory coordinates respectively.