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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Scifeed alert for new publications
Never miss any articles
matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
Define your Scifeed now
Share & Cite This Article
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.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.