Dynamics of classical solitons (in non-integrable systems)

Abstract A survey of the properties of soliton type solutions to non-linear wave equations appearing in various fields of physics is given. For the most part the description deals with non-integrable systems and remains at the classical level. Some general features associated with solitons-stationary states, bound states of solitons, stability, the Fermi-Pasta-Ulam problem, and so on are discussed for both one- and more-dimensional worlds. The results of computer experiments on the dynamics of the formation and interaction (in one-space-dimensional geometry) of soliton-type objects are presented at length. As an application of the general theory we speculate on solitons in plasmas and particle physics. Finally, new, spherically symmetric, oscillating solutions (“pulsons”) are examined in the framework of ϕ4 and sine-Gordon theories.