On the Algebra of -Deformed Pseudodifferential Operators

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 -deformed pseudodifferential operators. We use this algebraic structure to study in particular -Burgers and -KdV differential operators by the Lax generating technique. We give -deformed Lax equations as well as the report between these equations through the -deformed Burgers-KdV mapping.

On the Classical and Deformed Korteweg-de Vries Equation

“…By building a pair of Lax from one integrable Hamiltonian system, we obtain the solution of the system. Because the Lax equation is the equivalent of the dynamic system equation [10,11].…”

“…In this work, we investigate some properties related to this prototype nonlinear differential equation, based on the classical Q-deformation version and the interesting system KdV of the Moyal momentum deformation, and show how to reinforce its central role [10,11].…”

Note on q-deformed pseudo-differential operators and its supersymetric extension

“…Noting A s p,q the algebra of pseudo-differential operators PDO with three quantum numbers s,p and q describing respectively the conformal weight, the lower and higher degrees of type [1,2,3]…”