The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies
Exactly Solvable and Integrable Systems
2018-03-20 v1 Superconductivity
Mathematical Physics
math.MP
Abstract
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are obtained. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.
Keywords
Cite
@article{arxiv.1612.00239,
title = {The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies},
author = {K. Sabirov and S. Rakhmanov and D. Matrasulov and H. Susanto},
journal= {arXiv preprint arXiv:1612.00239},
year = {2018}
}