Chaos, Soliton And Chaotic Soliton In Josephson Junctions

For several decades, researches on chaos in Josephson junctions havebeen the focus of considerable attraction. Their intrinsic nonlinearityi and the interactions with externally applied fields make them a kind ofclassically chaotic systems. The known analytical methods can predict onset of some chaos in physical systems, however, can' t solve the nonlinear equations corresponding to chaotic systems. The direct perturbation technique, proposed recently, successfully deals with a kind of perturbed chaotic systems and obtains their general solutions for each order. Those are what our paper is based on.The paper consists of four parts. In the f i rst chaptei?introduction, we present the history and progress on chaos in Josephson junctions, also report the basic development, method about this paper. In the second chapter, we discuss some properties of chaos in a rf-current biasedJosephson junction with linear and quadratic damping respectively. Usingthe direct perturbation method, we gave the analytically chaotic solutionand its boundedness condition to each perturbed equation. Theoretical analysis manifested that the boundedness condition contained the famous Melnikov criteria of chaos. By numerical work, the time evolvement curves of the corrected solution, phase orbits and V-I characteristics demonstrated the deterministic chaos. The following chapter is on the solitons in Josephson transmission lines. We summary the important progress on them, such as the behavior and features of single soli ton in perturbed SG equation, the interaction of soli ton with environment, sol iton bunching and soli-ton exci tation et al. On the basis of the second and third chapters, we study the hyperradiation from soliton in chaotic state in the last chapter. For two coupled long Josephson junctions, we calculate the maximal emitted power which exceeded prediction value of the superradiation theory largely. Our investigations displayed that it is chaos to lead the radiation to the maximal value.The fourth chapter is fully the author' s work and the author has devoted part labor to the others.