@article{4cd0fbc624e14010910f55e636ab6040,

title = "The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies",

abstract = "We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. 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 = "Jacobi's elliptic functions, Metric graphs, The Gibbs free-energy functional, The star graph, The stationary sine-Gordon equation",

author = "K. Sabirov and S. Rakhmanov and D. Matrasulov and H. Susanto",

note = "Funding Information: We thank Dmitry Pelinovsky for his useful comments on the paper. This work is supported by a grant of the Volkswagen Foundation and by grants of the Agency for Science and Technology of Uzbekistan (Refs. No. F-2-003 and BF-2-022 ). HS would like to acknowledge The Physical Society of Uzbekistan for the invitation and partial financial support to attend a workshop in Tashkent organized by the society. Funding Information: We thank Dmitry Pelinovsky for his useful comments on the paper. This work is supported by a grant of the Volkswagen Foundation and by grants of the Agency for Science and Technology of Uzbekistan (Refs. No. F-2-003 and BF-2-022). HS would like to acknowledge The Physical Society of Uzbekistan for the invitation and partial financial support to attend a workshop in Tashkent organized by the society. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = apr,

day = "26",

doi = "10.1016/j.physleta.2017.12.057",

language = "British English",

volume = "382",

pages = "1092--1099",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier",

number = "16",

}