D.E. Pelinovsky and Y. Shimabukuro

Orbital stability of Dirac solitons

Letters in Mathematical Physics 104, 21-41 (2014)

We prove H1 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 H1 norm of the L2-small solutions of the massive Thirring model.

nonlinear Dirac equations, inverse scattering, stability of solitary waves, global existence