1306.5150 (Andrew Comech et al.)

Instability of Dirac--Maxwell solitary waves away from nonrelativistic
limit    [PDF]

Andrew Comech, Gregory Berkolaiko, Alim Sukhtayev

We derive a new criterion of instability of solitary waves and show that it plays an important role in the Dirac-type equations. For ground state solitary waves in the Dirac--Maxwell system, we conclude analytically that there is a critical value $\omega\sb\star\in(-m,m/2)$ such that the solitary waves with $\omega\in(\omega\sb\star,m)$ are linearly unstable. Comparison with the Dirac--Coulomb system allows to predict that $\omega\sb\star\approx 0.3m$.

View original: http://arxiv.org/abs/1306.5150