The talk discusses orbital stability of Dirac solitons in the integrable massive Thirring model in H1 and L2. Orbital stability in H1 is proven by working with an additional conserved quantity which
complements Hamiltonian, momentum and charge functionals of the general nonlinear Dirac equations. Orbital stability in L2 is proven by using local well posedness of the massive Thirring model in L2, conservation of the charge functional, and the auto-Backlund transformation.