Orbital stability of Dirac solitons

Abstract: We prove $H^1$ orbital stability of Dirac solitons in the integrable massive Thirring model by working with an additional conserved quantity which complements Hamiltonian, momentum and charge functionals of the general nonlinear Dirac equations. We also derive a global bound on the $H^1$ norm of the $L^2$-small solutions of the massive Thirring model.