{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T04:38:49Z","timestamp":1780375129149,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"EU","award":["PID2020-112620GB-I00"],"award-info":[{"award-number":["PID2020-112620GB-I00"]}]},{"name":"EU","award":["PID2022-143120OB-I00"],"award-info":[{"award-number":["PID2022-143120OB-I00"]}]},{"name":"EU","award":["PHY-2110030"],"award-info":[{"award-number":["PHY-2110030"]}]},{"name":"EU","award":["DMS-2204702"],"award-info":[{"award-number":["DMS-2204702"]}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["PID2020-112620GB-I00"],"award-info":[{"award-number":["PID2020-112620GB-I00"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["PID2022-143120OB-I00"],"award-info":[{"award-number":["PID2022-143120OB-I00"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["PHY-2110030"],"award-info":[{"award-number":["PHY-2110030"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2204702"],"award-info":[{"award-number":["DMS-2204702"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the existence of such structures, we bring to bear a combination of analysis-inspired numerical tools that permit the construction of such waveforms to a desired numerical accuracy. In addition, this enables us to explore their numerical stability. Our computations show that for the spatially heterogeneous form of the \u03d54 model considered herein, the breather solutions are generically unstable. Their instability seems to generically favor the motion of the relevant structures. We expect that these results may inspire further studies towards the identification of stable continuous breathers in spatially heterogeneous, continuum nonlinear wave equation models.<\/jats:p>","DOI":"10.3390\/e26090756","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T02:25:49Z","timestamp":1725416749000},"page":"756","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Stability of Breathers for a Periodic Klein\u2013Gordon Equation"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1184-5119","authenticated-orcid":false,"given":"Martina","family":"Chirilus-Bruckner","sequence":"first","affiliation":[{"name":"Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7162-5759","authenticated-orcid":false,"given":"Jes\u00fas","family":"Cuevas-Maraver","sequence":"additional","affiliation":[{"name":"Grupo de F\u00edsica No Lineal, Departamento de F\u00edsica Aplicada I, Universidad de Sevilla, Escuela Polit\u00e9cnica Superior, C\/Virgen de \u00c1frica, 7, 41011 Sevilla, Spain"},{"name":"Instituto de Matem\u00e1ticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis. Avda. 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