Nonlinear Dynamics of Globally Coupled Sine-Gordon Equations

摘要

This paper reports results of the systematic analysis of the dynamics of fluxons (kinks) in the fundamental prismatic configuration formed by three bulk superconductors, which creates a set of three parallel long Josephson junctions at interfaces between them. The setting is described by a system of three coupled sine-Gordon equations for the phases corresponding to each junction. In fact, the condition for the external magnetic flux trapped by the system reduces the model to two equations. The equations include the dissipative terms, and are controlled by the frustration parameter, that measures the deviation of the external flux from half a quantum. Analyzing the corresponding potential profile, we have identified different types of topological kink solitons, which correspond to fluxons, in terms of the coupled junctions. Nontopological 'bubble' modes have been found too. Some solutions, including those for 'compound' kinks and for two types of the bubbles, were obtained in an analytical form. Numerical simulations demonstrate that the compound kinks are unstable against breaking up into pairs of simple kinks. Bubbles are metastable objects, that eventually break up into kink-antikink pairs. The system also gives rise to kinks which connect different potential minima, hence they are pulled by the tilt of the potential. Using the momentum- balance method, we have derived the equilibrium velocity at which such driven kinks should move, and verified the prediction by simulations. Finally, collisions between the moving kinks were studied by means of direct simulations, which demonstrate that the collisions are always strongly inelastic.