On the algebra of \(q\)-deformed pseudodifferential operators (Q2396964)

Summary: While basing on the study that we we achieved on pseudodifferential operators in our works [with \textit{A. Zemate}, ``Super Gelfand-Dickey algebra and integrable models'', Chin. J. Phys. 47, No. 6, 764--787 (2009); with \textit{H. Erguig} and \textit{J. Zerouaoui}, Adv. Stud. Theor. Phys. 2, No. 1--4, 87--97 (2008; Zbl 1163.35039)], we interest in this paper to the construction of the algebra of \(q\)-deformed pseudodifferential operators. We use this algebraic structure to study in particular \(q\)-Burgers and \(q\)-KdV differential operators by the Lax generating technique. We give \(q\)-deformed Lax equations as well as the report between these equations through the \(q\)-deformed Burgers-KdV mapping.