We show that a system of Hirota bilinear equations introduced by Jimbo and Miwa defines tau-functions of the modified KP (MKP) hierarchy of evolution equations introduced by Dickey. Some other equivalent definitions of the MKP hierarchy are established. All polynomial tau-functions of the KP and the MKP hierarchies are found. Similar results are obtained for the reduced KP and MKP hierarchies.

中文翻译：

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MKP层次结构及其多项式tau函数的等价形式

我们展示了由Jimbo和Miwa引入的Hirota双线性方程组定义了由Dickey引入的改进的KP（MKP）演化方程的tau函数。建立了MKP层次结构的一些其他等效定义。找到KP和MKP层次结构的所有多项式tau函数。对于减少的KP和MKP层次结构，获得了相似的结果。