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We shall review orbital stability of solitons in the integrable Dirac equation known as the massive Thirring model. Orbital stability is obtained by using two different methods: one method relies on the higher-order energy conservation and the other one relies on the Backlund transformation. We shall also give numerical and analaytical results on the transverse stability of Dirac solitons under symmetry-breaking perturbations. Host: Avadh Saxena |