Noncommutative deformation of the Kadomtsev-Petviashvili hierarchy
The paper proposes a generalization of the Kadomtsev-Petviashvili hierarchy of exactly integrable PDEs to the case of a noncommutative space-time, in the spirit of the quantum group theory. The main objective of the work is to prove the existence and uniqueness for the corresponding noncommutative analog of the so-called Sato-Wilson equation. To this end, a differential calculus is built on the noncommutative space-time, and an algebra of pseudodifferential operators, related to the skew differentiation, is described, which allows to prove the completeness integrability theorem for the noncommutative Sato-Wilson equation.
scientific article; zbMATH DE number 1213205
scientific article