Soliton interactions and bound states

Abstract

The research presented in this thesis is concerned with soliton interactions and bound states. We consider a on-topological soliton in (1 + 1) dimensions and topological models in (2 + 1) and (3 + 1) dimensions. In chapter 2 we consider Qballs, which are non-topological solitons, in (1 + 1) dimensions. Here we note the semi-integrable behaviour of small-charge Qballs. This leads us to propose a possible mechanism to explain the two distinct oscillatory modes of a Qball breather. In chapter 3 we are interested in the (2+1)-dimensional baby-skyrme model, which is a lower-dimensional analogue of the Skyrme theory.
We discover new chain-like bound-state minimum-energy solutions. We then analyse whether these solutions are the minimum-energy solutions on a cylinder, and then finally on the torus. In chapter 4 we discuss a new (2 + 1)-dimensional model containing a baby skyrmion coupled to a vector meson. This is an analogue of the (3 + 1)-dimensional Skyrme theory containing a vector meson. We use this lower-dimensional analogue to numerically justify the use of a rational map ansatz in the analysis of the (3 + 1)-dimensional skyrmion. Also we analytically prove why the baby-skyrme model, and the model containing a baby skyrmion stabilised by a vector meson, have very similar solutions. Chapter 5 discusses Hopf solitons. Instead of being lumps, Hopf solitons actually resemble loops of string. Their charge is related to the string's knotting and twisting. In this chapter we include an extra mass term in the Skyrme-Faddeev theory; this gives solitons which are exponentially localised. We then explore the infinite-coupling case, which gives compact Hopons. This chapter is part of an ongoing investigation. All of the original research results presented are my own results.