Can Soliton Attractors Exist in Realistic 3+1-D Conservative Systems?

High-energy physicists already know that stable attractors (solitons) can exist in 3+1-dimensional conservative Lagrangian systems, so long as the definition of an attractor is based on weak notions of stability and the fields admit topological charge. This paper explores the possibility of attractors in Lagrangian field theories without topological charge, using a new, stronger concept of stability—Convective quantized Asymptotic Orbital Stability (ChAOS) . Under certain conditions, ChAOS is related to additive Liapunov stability or energetic stability. Russian physicists have argued that such stability tends to require topological charge; however, this paper describes systems which avoid those arguments, and suggests how numerical examples might be constructed. Solitons have been proposed to explain the existence and nature of elementary particles within the Feynman version of quantum theory; Section 6cites this literature, as well as new possibilities for alternative versions with testable nuclear implications.