On the Spectral Stability of Solitary Waves

Abstract

We study the spectral stability of the solitary wave solutions to the nonlinear Dirac equations. We focus on two types of nonlinearity: the Soler type and the Coulomb type. For the Soler model, we apply the Evans function technique to explore the point spectrum of the linearized operator at a solitary wave solution to the 2D and 3D cases. For the toy Coulomb model, the solitary wave solutions are no longer SU(1, 1) symmetric. We show numerically that there are no eigenvalues near 2ωi in the nonrelativistic limit (ω . m) and the spectral stability persists in spite of the absence of SU(1, 1) symmetry.