抄録
We study τ-function representation of solutions and deformation of Hirota bilinear relations for a noncommutative Kadomtsev–Petviashvili (NC KP) hierarchy. An operator-valued τ-function representation of solutions for the NC KP hierarchy is presented. In contrast to the commutative case, the admissible τ-function satisfies an additional triangle-like relation. Furthermore, instead of the commutative Hirota bilinear relations, a set of triple-product relations such as Hirota triple-product differential/difference equations is found. Noncommutative deformation of multi-line soliton solutions of the NC KP hierarchy is also investigated. It is shown that for an arbitrary noncommutative parameter, the corresponding operator-valued τ-function in general is expressed in the form of infinite series.
