{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T03:00:51Z","timestamp":1774062051897,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T00:00:00Z","timestamp":1550620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2017-R1C1B5-017743"],"award-info":[{"award-number":["NRF-2017-R1C1B5-017743"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u00f6dinger 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\u00f6dinger 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.<\/jats:p>","DOI":"10.3390\/sym11020271","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T11:45:39Z","timestamp":1550663139000},"page":"271","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Soliton and Breather Splitting on Star Graphs from Tricrystal Josephson Junctions"],"prefix":"10.3390","volume":"11","author":[{"given":"Hadi","family":"Susanto","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6859-447X","authenticated-orcid":false,"given":"Natanael","family":"Karjanto","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College, Sungkyunkwan University, Natural Science Campus, 2066 Seobu-ro, Jangan-gu, Suwon 16419, Gyeonggi-do, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Zulkarnain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Kampus Bina Widya KM 12.5, Simpang Baru, Tampan, Kota Pekanbaru, Riau 28293, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1116-9023","authenticated-orcid":false,"given":"Toto","family":"Nusantara","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Jalan Semarang 5, Malang 65145, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9560-3442","authenticated-orcid":false,"given":"Taufiq","family":"Widjanarko","sequence":"additional","affiliation":[{"name":"Manufacturing Metrology Team, Faculty of Engineering, The University of Nottingham, Advanced Manufacturing Building, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,20]]},"reference":[{"key":"ref_1","unstructured":"Pauling, L. 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