Nonlinear Wave Equations Related to Nonextensive Thermostatistics

We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive Sq entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2017-02, Vol.19 (2), p.60-60
Main Authors: Plastino, Angel R, Wedemann, Roseli S
Format: Article
Language:English
Subjects:
Entropy
Formalism
Klein-Gordon equation
Mathematical analysis
nonextensive entropies
nonextensive thermostatistics
nonlinear wave equations
Nonlinearity
Plane waves
Time dependence
Wave equations
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Summary:We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive Sq 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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e19020060