{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T13:26:08Z","timestamp":1777209968227,"version":"3.51.4"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,8,3]],"date-time":"2015-08-03T00:00:00Z","timestamp":1438560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\u00f6dinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schr\u00f6dinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schr\u00f6dinger\u2013Hirota\u2013Maxwell\u2013Bloch equations, along with their Lax pairs.<\/jats:p>","DOI":"10.3390\/sym7031352","type":"journal-article","created":{"date-parts":[[2015,8,5]],"date-time":"2015-08-05T03:18:55Z","timestamp":1438744735000},"page":"1352-1375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":68,"title":["Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials"],"prefix":"10.3390","volume":"7","author":[{"given":"Ratbay","family":"Myrzakulov","sequence":"first","affiliation":[{"name":"Eurasian International Center for Theoretical Physics and Department of General, Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan"}]},{"given":"Galya","family":"Mamyrbekova","sequence":"additional","affiliation":[{"name":"Eurasian International Center for Theoretical Physics and Department of General, Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan"}]},{"given":"Gulgassyl","family":"Nugmanova","sequence":"additional","affiliation":[{"name":"Eurasian International Center for Theoretical Physics and Department of General, Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan"}]},{"given":"Muthusamy","family":"Lakshmanan","sequence":"additional","affiliation":[{"name":"Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India"}]}],"member":"1968","published-online":{"date-parts":[[2015,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1098\/rsta.2010.0319","article-title":"The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview","volume":"369","author":"Lakshmanan","year":"2011","journal-title":"Phil. 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