Nonlinear chiral models: Soliton solutions and spatio-temporal chaos

Abstract

Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.