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
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
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.
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MDPI and ACS Style
Plastino, A.R.; Wedemann, R.S. Nonlinear Wave Equations Related to Nonextensive Thermostatistics. Entropy 2017, 19, 60.
Plastino AR, Wedemann RS. Nonlinear Wave Equations Related to Nonextensive Thermostatistics. Entropy. 2017; 19(2):60.
Plastino, Angel R.; Wedemann, Roseli S. 2017. "Nonlinear Wave Equations Related to Nonextensive Thermostatistics." Entropy 19, no. 2: 60.
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