{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T23:42:50Z","timestamp":1791070970697,"version":"4.1.0"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We present a numerical study of the self-similar solutions of the localized induction approximation of a vortex filament. These self-similar solutions, which are explicitly known, constitute a one-parameter family and develop a singularity in finite time. We study a number of boundary conditions that allow us to reproduce the mechanism of singularity formation. Some related questions are also considered.<\/jats:p>","DOI":"10.1137\/080741720","type":"journal-article","created":{"date-parts":[[2009,9,2]],"date-time":"2009-09-02T18:06:52Z","timestamp":1251914812000},"page":"1047-1077","source":"Crossref","is-referenced-by-count":18,"title":["A Numerical Study of the Self-Similar Solutions of the Schr\u00f6dinger Map"],"prefix":"10.1137","volume":"70","author":[{"given":"F.","family":"de la Hoz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C. J.","family":"Garc\u00eda-Cervera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Vega","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,9,2]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1761268"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0732037"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2007.03.007"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-008-0682-3"},{"key":"R5","unstructured":"G. K. Batchelor,\n                      An Introduction to Fluid Dynamics\n                      , Cambridge Math. Lib., Cambridge University Press, Cambridge, UK, 1967."},{"key":"R6","unstructured":"T. F. Buttke,\n                      A Numerical Study of Superfluid Turbulence in the Self-Induction Approximation\n                      , Ph.D. thesis, University of California, Berkeley, 1986."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90145-3"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang,\n                      Spectral Methods in Fluid Dynamics\n                      , Springer Ser. Comput. Phys., Springer-Verlag, New York, 1988.","DOI":"10.1007\/978-3-642-84108-8"},{"key":"R9","unstructured":"I. Cimr\u00e1k,\n                      On the Landau-Lifshitz Equation of Ferromagnetism\n                      , Ph.D. thesis, Ghent University, Ghent, Belgium, 2005."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF03018608"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-007-0115-6"},{"key":"R12","unstructured":"P. G. Drazin and R. S. Johnson,\n                      Solitons: An Introduction\n                      , Cambridge University Press, Cambridge, UK, 1992."},{"key":"R13","doi-asserted-by":"crossref","unstructured":"M. V. Dyke,\n                      An Album of Fluid Motion\n                      , Parabolic Press, Stanford, CA, 1982.","DOI":"10.1115\/1.3241909"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999352199"},{"key":"R15","unstructured":"B. Fornberg,\n                      A Practical Guide to Pseudospectral Methods\n                      , Cambridge University Press, Cambridge, UK, 1998."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2004.840301"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6793"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1109\/TMAG.2006.872199"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"D. Gottlieb and S. A. Orszag,\n                      Numerical Analysis of Spectral Methods: Theory and Applications\n                      , CBMS-NSF Reg. Conf. Ser. Appl. Math. 26 SIAM, Philadelphia, 1977.","DOI":"10.1137\/1.9781611970425"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-120021181"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112072002307"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1170"},{"key":"R23","unstructured":"J. D. Lambert,\n                      Computational Methods in Ordinary Differential Equations\n                      , Introductory Mathematics for Scientists and Engineers, John Wiley & Sons, London, New York, Sydney, 1973."},{"key":"R24","first-page":"153","volume":"8","author":"Landau L. D.","year":"1935","journal-title":"Phys. Z. Sowjetunion","ISSN":"https:\/\/id.crossref.org\/issn\/0369-9811","issn-type":"print"},{"key":"R25","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1017\/S0022112002003282","volume":"477","author":"Lipniacki T.","year":"2002","journal-title":"J. Fluid Mech.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-1120","issn-type":"print"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1063\/1.1566756"},{"key":"R27","unstructured":"ONERA,\n                      A\u00e9rodynamique: d\u00e9collement\n                      3\n                      D et tourbillons. Tourbillons sur une aile delta en incidence\n                      , http:\/\/www.onera.fr\/conferences\/decollement3d\/17-tourbillonsailedeltaincidence. html (2004)."},{"key":"R28","unstructured":"P. G. Saffman,\n                      Vortex Dynamics\n                      , Cambridge Monogr. Mech. Appl. Math., Cambridge University Press, New York, 1992."},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.31.5782"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1007\/BF01220998"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080741720","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:11:40Z","timestamp":1787335900000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080741720"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/080741720"],"URL":"https:\/\/doi.org\/10.1137\/080741720","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}