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      Soliton and breather splitting on star graphs from tricrystal Josephson junctions

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          Abstract

          We consider the interactions of traveling localized wave solutions with a vertex in a star graph domain that describes multiple Josephson junctions with a common/branch point (i.e., tricrystal junctions). The system is modeled by the sine-Gordon equation. The vertex is represented by boundary conditions that are determined by the continuity of the magnetic field and vanishing total fluxes. When one considers small-amplitude breather solutions, the system can be reduced into the nonlinear Schr\"odinger equation posed on a star graph. Using the equation, we show that a high-velocity incoming soliton is split into a transmitted component and a reflected one. The transmission is shown to be in good agreement with the transmission rate of plane waves in the linear Schr\"odinger equation on the same graph (i.e., a quantum graph). In the context of the sine-Gordon equation, small-amplitude breathers show similar qualitative behaviors, while large-amplitude ones produce complex dynamics.

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          Most cited references19

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          Logic design of Josephson network

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            Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph

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              Interaction of discrete breathers with impurity modes

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                Author and article information

                Journal
                11 June 2019
                Article
                10.3390/sym11020271
                1906.04901
                1bb2ce63-3cb4-4ac9-af0b-771174fcf2ed

                http://creativecommons.org/licenses/by/4.0/

                History
                Custom metadata
                35C08, 35L53, 35L60, 35L70, 35Q51, 35Q55, 37K40
                Symmetry 11 (2019) 271
                10 pages, 4 figures
                nlin.PS cond-mat.supr-con

                Condensed matter,Nonlinear & Complex systems
                Condensed matter, Nonlinear & Complex systems

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