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 f ields admit topological charge. This paper explores the possibility of attr actors in Lagrangian field theories without topological charge, using a new , stronger concept of stability-Convective quantized Asymptotic Orbital Sta bility (ChAOS). Under certain conditions, ChAOS is related to 'additive Lia punov stability' or energetic stability. Russian physicists have argued tha t such stability tends to require topological charge; however, this paper d escribes systems which avoid those arguments, and suggests how numerical ex amples might be constructed. 'Solitons' have been proposed to explain the e xistence and nature of elementary particles within the Feynman version of q uantum theory; Section 6 cites this literature, as well as new possibilitie s for alternative versions with testable nuclear implications. (C) 1999 Pub lished by Elsevier Science Ltd. All rights reserved.