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Entropy 2017, 19(1), 21;

Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations

La Plata National University and Argentina’s National Research Council, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina
Faculty of Exact and Natural Sciences, La Pampa National University, Uruguay 151, Santa Rosa, 3300 La Pampa, Argentina
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 5 November 2016 / Revised: 28 December 2016 / Accepted: 29 December 2016 / Published: 31 December 2016
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Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27)). It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1 ) or with its NRT non-linear q-generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q 1 instance via a perturbative analysis of the NRT equations. View Full-Text
Keywords: non-linear Schrödinger equation; non-linear Klein–Gordon equation; first order solution non-linear Schrödinger equation; non-linear Klein–Gordon equation; first order solution

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Zamora, J.; Rocca, M.C.; Plastino, A.; Ferri, G.L. Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations. Entropy 2017, 19, 21.

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