We show that spinor systems with scalar self-interaction, such as the Dirac-Klein-Gordon system with Yukawa coupling or the Soler model, generically have bi-frequency solitary wave solutions. We develop the approach to stability properties of such waves and use the radial reduction to show that indeed the (linear) stability is available for a wide range of parameters. We show that only bi-frequency modes can be dynamically stable and suggest that stable bi-frequency modes can serve as storages of the Dark Matter. The approach is based on linear stability results of one-frequency solitary waves in (3+1)D Soler model, which we obtain as a by-product.

The U.S. military is a significant contributor to the climate crisis and other sustainability concerns. However, there is very limited research on how changes in U.S. military spending directly impact...