Soliton dynamics in nonlinear planar systems

Abstract

The work in this thesis is concerned with the study of stability and scattering of solitons in planar models ie where spacetime is (2+l)-dimensional. We consider both integrable models, where exact solutions can be written in closed form, and non-integrable models, where approximations and numerical methods must be employed. In chapter III we use a 'collective coordinate' approximation to study the scattering of solitons in a model motivated by elementary particle physics. In chapter IV we discuss a method to obtain approximate soliton configurations which can then be used to investigate soliton dynamics. In chapter V we perform a test of the 'collective coordinate' approximation by applying it to the study of classical and quantum soliton scattering in an integrable model, where exact results are known. Chapters VI and VII are concerned with an integrable chiral model. First we construct exact solutions using twistor methods and then we go on to study soliton stability using numerical techniques. Through computer simulations we find that there exist solitons which scatter in a way unlike any previously found in integrable models. Furthermore, this soliton scattering resembles very closely that found in certain non-integrable models, thereby providing a link between the two classes. Finally, chapter VIII is an outlook on current and future research.