{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T13:41:48Z","timestamp":1768484508038,"version":"3.49.0"},"reference-count":52,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T00:00:00Z","timestamp":1567296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004564","name":"Ministarstvo Prosvete, Nauke i Tehnolo\u0161kog Razvoja","doi-asserted-by":"publisher","award":["ON171017"],"award-info":[{"award-number":["ON171017"]}],"id":[{"id":"10.13039\/501100004564","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.<\/jats:p>","DOI":"10.3390\/sym11091090","type":"journal-article","created":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T03:16:12Z","timestamp":1567394172000},"page":"1090","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5735-3198","authenticated-orcid":false,"given":"Du\u0161an","family":"Vudragovi\u0107","sequence":"first","affiliation":[{"name":"Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5435-1688","authenticated-orcid":false,"given":"Antun","family":"Bala\u017e","sequence":"additional","affiliation":[{"name":"Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1038\/nature06036","article-title":"Strong dipolar effects in a quantum ferrofluid","volume":"448","author":"Lahaye","year":"2007","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"190401","DOI":"10.1103\/PhysRevLett.107.190401","article-title":"Strongly dipolar Bose-Einstein condensate of dysprosium","volume":"107","author":"Lu","year":"2011","journal-title":"Phys. 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