Chaotic solitons in conservative systems: Can they exist?

Abstract

Chaotic solitons (“chaoitons”) are essentially just the localized attractors generated by PDE. If truly chaotic chaoitons can exist in simple conservative systems, then the potential implications for physics and biology may be very important. Using a simple test for attractors, I find that they can exist there only in systems which appear capable of multifurcation (lack of definedness in dynamics). A simple Lagrangian is proposed for further study. There is a substantial need for new computer-based research in this area.