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arXiv · 0904.1868

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

Liu Shaowei·He Jingsong·Cheng Yi
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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 $τ^{(n+k)}_\triangle$ of the dKP hierarchy from an initial $τ_\triangle$. In this process, we introduce a generalized discrete Wronskian determinant and some useful properties of discrete difference operator.

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Liu Shaowei, He Jingsong, Cheng Yi. 2010-01-05. The determinant representation of the gauge transformation for the discrete KP hierarchy. https://arxiv.org/abs/0904.1868

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