Orbital stability of Dirac solitons

TL;DR

This paper proves the orbital stability of Dirac solitons in the massive Thirring model using conserved quantities and establishes a global bound on small solutions' norms.

Contribution

It introduces a novel approach utilizing an additional conserved quantity to prove stability of Dirac solitons in an integrable model.

Findings

Proves $H^1$ orbital stability of Dirac solitons.

Derives a global bound on the $H^1$ norm of small solutions.

Enhances understanding of solution behavior in the massive Thirring model.

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.