Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks

Abstract

We consider discrete sine-Gordon equation on branched domains. The latter is modeled in terms of the metric graphs with discrete bonds having the form of the branched 1D chains. Exact analytical solutions of the problem are obtained for special case of the constraints given in terms of a simple sum rule. Numerical solution is obtained when the constraint is not fulfilled. A simple model of a Josephson junction network is proposed using the obtained results.