Dynamics of topological solitons in models with nonlocal interactions

Abstract

A nondissipative generalization of the sine-Gordon equation to cases with nonlocal interactions is analyzed. A model of this sort is shown to describe signal propagation in a Josephson transmission line with a nonlocal inductive coupling. The incorporation of nonlocal interactions changes the properties of the model in a qualitative way, leading in particular to the appearance of some new soliton entities: 2kpi kinks, where k greater, similar 1. These entities do not arise in a local model. They are evolutionary, they interact with each other in a quasielastic fashion, and they can be generated in a corresponding transmission line.