{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:51:35Z","timestamp":1774435895384,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,11]]},"abstract":"<jats:p> In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and\/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations. <\/jats:p>","DOI":"10.1142\/s0218127414501478","type":"journal-article","created":{"date-parts":[[2014,11,28]],"date-time":"2014-11-28T16:50:32Z","timestamp":1417193432000},"page":"1450147","source":"Crossref","is-referenced-by-count":5,"title":["Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials"],"prefix":"10.1142","volume":"24","author":[{"given":"M.","family":"Agaoglou","sequence":"first","affiliation":[{"name":"Department of Mathematics, Physics Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece"}]},{"given":"V. M.","family":"Rothos","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Physics Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece"}]},{"given":"D. J.","family":"Frantzeskakis","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece"}]},{"given":"G. P.","family":"Veldes","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece"}]},{"given":"H.","family":"Susanto","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK"}]}],"member":"219","published-online":{"date-parts":[[2014,11,28]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-52803-3"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/mop.23122"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.036608"},{"key":"rf4","series-title":"Nonlinear Systems and Complexity","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-02057-0_17","volume-title":"Localized Excitations in Nonlinear Complex Systems","volume":"7","author":"Diblik J.","year":"2014"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.01.042"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1063\/1.1814428"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1063\/1.2828176"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1126\/science.1177031"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1063\/1.3356223"},{"key":"rf10","volume-title":"Classical Electrodynamics","author":"Jackson J. 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