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Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview
Open AccessArticle

Nonlinear Wave Equations Related to Nonextensive Thermostatistics

CeBio y Secretaría de Investigación, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA-Conicet, Roque Saenz Peña 456, 6000 Junin, Argentina
Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, 20550-900 Rio de Janeiro, Brazil
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Entropy 2017, 19(2), 60;
Received: 25 December 2016 / Revised: 31 January 2017 / Accepted: 4 February 2017 / Published: 7 February 2017
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–Gordon, 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–Gordon equation. The other equation we study is a nonlinear Schroedinger-like equation. View Full-Text
Keywords: nonlinear wave equations; nonextensive entropies; nonextensive thermostatistics nonlinear wave equations; nonextensive entropies; nonextensive thermostatistics
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Plastino, A.R.; Wedemann, R.S. Nonlinear Wave Equations Related to Nonextensive Thermostatistics. Entropy 2017, 19, 60.

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