Table of Contents
ISRN High Energy Physics
Volume 2012 (2012), Article ID 503621, 12 pages
http://dx.doi.org/10.5402/2012/503621
Research Article

On the Algebra of π‘ž -Deformed Pseudodifferential Operators

Département de Physique, Laboratoire des Hautes Energies, Sciences de l'Ingénierie et Réacteurs (LHESIR), Faculté des Sciences, Université Ibn Tofail, Kénitra, Morocco

Received 14 December 2011; Accepted 4 January 2012

Academic Editor: A. Belhaj

Copyright © 2012 Abderrahman EL Boukili and Moulay Brahim Sedra. 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.

Abstract

While basing on the study that we we achieved on pseudodifferential operators in the works [arXiv:0708.4046 and hep-th/0610056 ], we interest in this paper to the construction of the algebra of π‘ž -deformed pseudodifferential operators. We use this algebraic structure to study in particular π‘ž -Burgers and π‘ž -KdV differential operators by the Lax generating technique. We give π‘ž -deformed Lax equations as well as the report between these equations through the π‘ž -deformed Burgers-KdV mapping.