{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:14:22Z","timestamp":1766268862371},"reference-count":59,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:p> The subject of moving curves (and surfaces) in three-dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc. Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution equations for moving surfaces are often intimately related to soliton equations in higher dimensions. <\/jats:p>","DOI":"10.1142\/s0218127405012004","type":"journal-article","created":{"date-parts":[[2005,3,17]],"date-time":"2005-03-17T11:46:57Z","timestamp":1111060017000},"page":"51-63","source":"Crossref","is-referenced-by-count":7,"title":["NONLINEAR DYNAMICS OF MOVING CURVES AND SURFACES: APPLICATIONS TO PHYSICAL SYSTEMS"],"prefix":"10.1142","volume":"15","author":[{"given":"S.","family":"MURUGESH","sequence":"first","affiliation":[{"name":"Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirappalli 620 024, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"LAKSHMANAN","sequence":"additional","affiliation":[{"name":"Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirappalli 620 024, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Solitons, Nonlinear Evolution Equations and Inverse Scattering","author":"Ablowitz M. J.","year":"1992"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4147-6"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.4174"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.2107"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"3108","DOI":"10.1103\/PhysRevB.47.3108","volume":"47","author":"Balakrishnan R.","journal-title":"Phys. Rev."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0045993"},{"key":"rf7","volume-title":"An Introduction to Fluid Dynamics","author":"Batchelor G. K.","year":"1967"},{"key":"rf8","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1098\/rspa.1984.0023","volume":"392","author":"Berry M. V.","journal-title":"Proc. Roy. Soc. London"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1038\/326277a0"},{"key":"rf10","volume-title":"Dynamics of Polymeric Liquids","author":"Bird R. B.","year":"1977"},{"key":"rf11","volume-title":"Fronts, Interfaces and Patterns","author":"Bishop A. R.","year":"1984"},{"key":"rf12","first-page":"S23","volume":"5","author":"Bretin V.","journal-title":"J. Opt."},{"key":"rf13","volume-title":"Principles of Condensed Matter Physics","author":"Chaikin P. M.","year":"1970"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.57.933"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.82.1554"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.65.851"},{"key":"rf17","volume-title":"Turbulence","author":"Frisch U.","year":"1996"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.67.3203"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.1094"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.5232"},{"key":"rf21","first-page":"3183","volume":"455","author":"Goriely A.","journal-title":"Proc. Roy. Soc. Lond."},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.1564"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/s003320010009"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1364\/OL.11.000730"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112072002307"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1038\/295393a0"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.72.33"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623981"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.74.953"},{"key":"rf30","volume-title":"Introduction to Solid State Physics","author":"Kittel C.","year":"1960"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1002\/sapm19969619"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(90)90130-T"},{"key":"rf33","first-page":"934","volume":"37","author":"Kugler M.","journal-title":"Phys. Rev."},{"key":"rf34","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/0378-4371(76)90106-0","volume":"84","author":"Lakshmanan M.","journal-title":"Physica"},{"key":"rf35","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0375-9601(77)90262-6","volume":"61","author":"Lakshmanan M.","journal-title":"Phys. Lett."},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1063\/1.524273"},{"key":"rf37","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0375-9601(79)90290-1","volume":"75","author":"Lakshmanan M.","journal-title":"Phys. Lett."},{"key":"rf38","doi-asserted-by":"publisher","DOI":"10.1007\/BF00382623"},{"key":"rf39","doi-asserted-by":"publisher","DOI":"10.1063\/1.532466"},{"key":"rf40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-55688-3"},{"key":"rf41","doi-asserted-by":"publisher","DOI":"10.1063\/1.523453"},{"key":"rf42","first-page":"153","volume":"8","author":"Landau L.","journal-title":"Phys. Z. Sowjet"},{"key":"rf43","volume-title":"On Some Integrable and Nonintegrable Soliton Equations of Magnets I-IV","author":"Myrzakulov R.","year":"1987"},{"key":"rf44","doi-asserted-by":"publisher","DOI":"10.1063\/1.532279"},{"key":"rf45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.69.2603"},{"key":"rf46","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.62.1895"},{"key":"rf47","volume-title":"Dynamics of Curved Fronts","author":"Pelce P.","year":"1986"},{"key":"rf48","doi-asserted-by":"publisher","DOI":"10.1063\/1.529086"},{"key":"rf49","doi-asserted-by":"publisher","DOI":"10.1063\/1.1589155"},{"key":"rf50","volume-title":"Vortex Dynamics","author":"Saffman P. G.","year":"1992"},{"key":"rf51","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626319"},{"key":"rf52","doi-asserted-by":"crossref","first-page":"2398","DOI":"10.1103\/PhysRevB.38.2398","volume":"38","author":"Schwarz K. W.","journal-title":"Phys. Rev."},{"key":"rf53","volume-title":"Geometric Phases in Physics","author":"Shapere A.","year":"1989"},{"key":"rf54","first-page":"155","volume":"98","author":"Spruit H. C.","journal-title":"Astron. Astrophys."},{"key":"rf55","volume-title":"Differential Geometry","author":"Stoker J. J.","year":"1969"},{"key":"rf56","volume-title":"Lectures on Classical Differential Geometry","author":"Struik D. J.","year":"1961"},{"key":"rf57","volume-title":"Geometric Aspects of the Einstein Equations and Integrable Systems","author":"Sym A.","year":"1985"},{"key":"rf58","volume-title":"When Time Breaks Down","author":"Winfree A. T.","year":"1987"},{"key":"rf59","first-page":"118","volume":"61","author":"Zakharov V. E.","journal-title":"Zh. Eksp. I Theor. Fiz."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012004","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:06:35Z","timestamp":1565136395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1]]},"references-count":59,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,1]]}},"alternative-id":["10.1142\/S0218127405012004"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012004","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1]]}}}