The massive Thirring model in physical coordinates is an integrable system of Dirac type that possess Dirac solitons as saddle points of the energy function. By using the local well-posedness in $L^2(\mathbb{R})$, conservation of the charge functional, and the auto-Backlund transformation, we have proved orbital stability of Dirac solitons in $L^2(\mathbb{R})$.

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.