We consider the branched Josephson junction created by planar superconductors connected to each other through the Y-junction insulator. Assuming that the structure interacts with the external constant magnetic field, we study static sine-Gordon solitons in such system by modeling them in terms of the stationary sine-Gordon equation on metric graph. Exact analytical solutions of the problem are obtained and their stability is analyzed.

中文翻译：

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分支的约瑟夫逊结：外部磁场中的载流孤子

我们考虑由平面超导体通过Y结绝缘体相互连接而创建的分支约瑟夫森结。假设结构与外部恒定磁场相互作用，我们通过在度量图上的静态正弦-戈登方程对它们进行建模，从而研究此类系统中的静态正弦-戈登孤子。获得了该问题的精确解析解，并对其稳定性进行了分析。