{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:57Z","timestamp":1760245077775,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,2,7]],"date-time":"2017-02-07T00:00:00Z","timestamp":1486425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive     S q     entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed for the Schroedinger, Klein\u2013Gordon, and Dirac wave equations. These previously introduced equations share the interesting feature of admitting q-plane wave solutions. In contrast with these recent developments, one of the nonlinear wave equations that we propose exhibits real q-Gaussian solutions, and the other one admits exponential plane wave solutions modulated by a q-Gaussian. These q-Gaussians are q-exponentials whose arguments are quadratic functions of the space and time variables. The q-Gaussians are at the heart of nonextensive thermostatistics. The wave equations that we analyze in this work illustrate new possible dynamical scenarios leading to time-dependent q-Gaussians. One of the nonlinear wave equations considered here is a wave equation endowed with a nonlinear potential term, and can be regarded as a nonlinear Klein\u2013Gordon equation. The other equation we study is a nonlinear Schroedinger-like equation.<\/jats:p>","DOI":"10.3390\/e19020060","type":"journal-article","created":{"date-parts":[[2017,2,7]],"date-time":"2017-02-07T12:08:18Z","timestamp":1486469298000},"page":"60","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Nonlinear Wave Equations Related to Nonextensive Thermostatistics"],"prefix":"10.3390","volume":"19","author":[{"given":"Angel","family":"Plastino","sequence":"first","affiliation":[{"name":"CeBio y Secretar\u00eda de Investigaci\u00f3n, Universidad Nacional del Noroeste de la Prov\u00edncia de Buenos Aires, UNNOBA-Conicet, Roque Saenz Pe\u00f1a 456, 6000 Junin, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7532-3881","authenticated-orcid":false,"given":"Roseli","family":"Wedemann","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, 20550-900 Rio de Janeiro, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1765","DOI":"10.3390\/e13101765","article-title":"The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks","volume":"13","author":"Tsallis","year":"2011","journal-title":"Entropy"},{"key":"ref_2","unstructured":"Tsallis, C. 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