On the Algebra of q-Deformed Pseudodifferential Operators

Abstract EN

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 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.