title：inverse scattering for derivative nls and massive thirring model
abstract：the massive thirring model in physical coordinates is an integrable system of dirac type that process dirac solitons as saddle points of the energy function. by using the local well-posedness in spaces of squared integrable functions, conservation of the charge functional, and the auto-backlund transformation, we have proved orbital stability of dirac solitons. we also developed the inverse scattering transform and obtained the long-time scattering asymptotics for the massive thirring model in physical coordinates. these results rely on the recent development in the inverse scattering transform for the kaup-newell spectral problem. the reconstruction of the potential is performed separately in the limits $\lambda \to 0$ and $\lambda \to \infty$, where $\lambda$ is the spectral parameter of the kaup-newell spectral problem.
