On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D

Abstract

For the nonlinear Dirac equation with scalar self-interaction (the Soler model) in three spatial dimensions, we consider the linearization at solitary wave solutions and find the invariant spaces which correspond to different spherical harmonics, thus achieving the radial reduction of the spectral stability analysis. We apply the same technique to the bi-frequency solitary waves (which are generically present in the Soler model) and show that they can also possess linear stability properties similar to those of one-frequency solitary waves.