Interaction Between Solitons And Between A Soliton And An Impurity

Numerical simulations and experiments, it was revealed that solitons can mutually punctuate through each other like mass point, remaining their own features. Later, a very sophisticated method, namely, the method of inverse scattering transformation, was developed to commonly solve nonlinear equations possessing the solution of solitons.From the physical picture and mathematical results mentioned above, we study the problem of solitons' interaction which is not only valuable for dynamics of solitons, but also set a basic limit for soliton communication in optical fibers. Moreover, in the most recent years, a fantastic prospect of controlling chaos was demonstrated in a typical nonlinear system due to the cooperation of solitons and disorder. In the present paper, grounding on the convincing pictures of soliton, we begin with studying the interaction between solitons, definitely setting forth the physical mechanism of collision between solitons. Secondly, we thoroughly investigate an array of parametrically driven nonlinear oscillators, in which spatiotemporal patterns are formed despite the chaotic parameters when both solitons and impurities are present. By the virtue of method of multiple scales, we have derived the amplitude equation. The paper has been organized as following: in the part of introduction, we roughly describe the general picture the nonlinear science. This part consists of history of studying chaos and soliton, intuitive illustration about their concept and important application. In the first chapter, the fundamental results on the theory of solitons, along with related techniques in mathematics and experiment are introduced. The following two chapters deal with the problem of interactionbetween solitons and between solitons and impurities, respectively. We spend the last chapter on summary and prospect about theory of solitons.