$L^2$ orbital stability of Dirac solitons in the massive Thirring model

Abstract

We prove $L^2$ orbital stability of Dirac solitons in the massive Thirring model. Our analysis uses local well posedness of the massive Thirring model in $L^2$, conservation of the charge functional, and the auto--Bäcklund transformation. The latter transformation exists because the massive Thirring model is integrable via the inverse scattering transform method.

References in corpus (3)

• On the meaning of the Vakhitov-Kolokolov stability criterion for the nonlinear Dirac equation
• Linear instability of nonlinear Dirac equation in 1D with higher order nonlinearity
• Stability of multi-solitons in the cubic NLS equation

Cited by in corpus (4)

• Solitary waves of a PT-symmetric Nonlinear Dirac equation
• Global well-posedness for the massless cubic Dirac equation
• Solitary waves in the Nonlinear Dirac Equation
• Integrable semi-discretization of the massive Thirring system in laboratory coordinates