The determinant representation of the gauge transformation for the discrete KP hierarchy

Abstract

A successive gauge transformation operator $T_{n+k}$ for the discrete KP(dKP) hierarchy is defined, which is involved with two types of gauge transformations operators. The determinant representation of the $T_{n+k}$ is established,and then it is used to get a new $tau$ function ${\tau }_{△}^{(n+k)}$ of the dKP hierarchy from an initial ${\tau }_{△}$. In this process, we introduce a generalized discrete Wronskian determinant and some useful properties of discrete difference operator.

15pages,to appear Science in China Ser A: Mathematics(2010)

References in corpus (1)

• On Darboux-Bäcklund Transformations for the Q-Deformed Korteweg-de Vries Hierarchy

Cited by in corpus (2)

• Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy
• The integral type gauge transformation and the additional symmetry for the constrained KP hierarchy