The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies
K.K. SabirovTashkent University of Information Technologies, Amir Temur Avenue 108, Tashkent, 100200, UzbekistanS. RakhmanovTurin Polytechnic University in Tashkent, 17 Kichik Xalka Yuli str., 100095, Tashkent, UzbekistanD. U. MatrasulovTurin Polytechnic University in Tashkent, 17 Kichik Xalka Yuli str., 100095, Tashkent, UzbekistanH. SusantoDepartment of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK#TAB#
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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.
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