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

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

2009-04-12

arxiv.org/abs/0904.1868v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

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 $\tau^{(n+k)}_\triangle$ of the dKP hierarchy from an initial $\tau_\triangle$. In this process, we introduce a generalized discrete Wronskian determinant and some useful properties of discrete difference operator.

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