Soliton and breather splitting on star graphs from tricrystal Josephson junctions

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

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 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.

Citation

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. https://doi.org/10.3390/sym11020271

• 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
• DOI: https://doi.org/10.3390/sym11020271
• Keywords: Soliton; Breather; Sine-Gordon equation; Schrödinger equation; Star graph; Quantum graph
• Public URL: https://nottingham-repository.worktribe.com/output/1693333
• Publisher URL: https://www.mdpi.com/2073-8994/11/2/271
• Additional Information: Invited paper for first author. My contribution is on initial simulation coding.