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Soliton and breather splitting on star graphs from tricrystal Josephson junctions

Susanto, Hadi; Karjanto, Natanael; Zulkarnain; Nusantara, Toto; Widjanarko, Taufiq


Hadi Susanto

Natanael Karjanto


Toto Nusantara

Taufiq Widjanarko


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 Schrödinger 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 Schrödinger 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.


Susanto, H., Karjanto, N., Zulkarnain, Nusantara, T., & Widjanarko, T. (2019). Soliton and breather splitting on star graphs from tricrystal Josephson junctions. Symmetry, 11(2), Article 271.

Journal Article Type Article
Acceptance Date Feb 12, 2019
Online Publication Date Feb 20, 2019
Publication Date Feb 20, 2019
Deposit Date Mar 27, 2019
Publicly Available Date Mar 28, 2019
Journal Symmetry
Electronic ISSN 2073-8994
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 11
Issue 2
Article Number 271
Keywords Soliton; Breather; Sine-Gordon equation; Schrödinger equation; Star graph; Quantum graph
Public URL
Publisher URL
Additional Information Invited paper for first author. My contribution is on initial simulation coding.


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