Next Article in Journal
Misalignment Fault Diagnosis of DFWT Based on IEMD Energy Entropy and PSO-SVM
Next Article in Special Issue
Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism
Previous Article in Journal
Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems
Previous Article in Special Issue
A Dissipation of Relative Entropy by Diffusion Flows
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(1), 21; doi:10.3390/e19010021

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

1
La Plata National University and Argentina’s National Research Council, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina
2
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
View Full-Text   |   Download PDF [549 KB, uploaded 31 December 2016]   |  

Abstract

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
Figures

Figure 1

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

SciFeed Share & Cite This Article

MDPI and ACS Style

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.

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.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top