$L^2$ orbital stability of Dirac solitons in the massive Thirring model

Abstract

We prove $L^2$ orbital stability of Dirac solitons in the massive Thirring model. Our analysis uses local well posedness of the massive Thirring model in $L^2$, conservation of the charge functional, and the auto--B\"{a}cklund transformation. The latter transformation exists because the massive Thirring model is integrable via the inverse scattering transform method.