Quantization of spin direction for solitary waves in a uniform magnetic field

It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data) and have nonzero spin (nonzero intrinsic angular momentum in the center of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein–Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or anti-parallel to the magnetic field direction.