The Analysis Of Non-topological Solitons Model

In this thesis, we systematically introduced the Q-ball theory, including the formation theory, the conditions of stability and the significance of experimental observations. There are three models in our study, they are complex Signum-Gordon model, the Boson stars with global magnetic monopole and the supersymmetric Q-ball model under finite temperature. Through respectively discussed the properties for each models in very large and very small radius, we gived the reliable analysis formula of the Q-ball radius and the minimum energy, rather than the numerical solution of specific values. It reveals the stable radius of Q-ball model,a relation between topological charge and the lowest energy.We solved the difficult problem in the past that non-topological soliton model describes the nonlinear differential equations, given a reliable analytical results, the model is compared with the objects and create the conditions for observation.The results'general form has a great significance for description of dark matter.For the supersymmetric Q-ball model under finite temperature,we calculated that this model was unstable after the expansion of the universe as the temperature drop in the early universe.