Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions

IF 1.8 3区数学 Q1 MATHEMATICS

Japanese Journal of Mathematics Pub Date : 2018-07-15 DOI:10.1007/s11537-018-1803-1

Victor G. Kac, Johan W. van de Leur

引用次数: 27

Abstract

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.

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MKP层次及其多项式函数的等价性

我们证明了Jimbo和Miwa引入的Hirota双线性方程组定义了Dickey引入的进化方程的改进KP (MKP)层次的tau函数。建立了MKP层次结构的一些其他等效定义。找到了KP和MKP层次的所有多项式τ函数。对于简化的KP和MKP层次，也得到了类似的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Japanese Journal of Mathematics 数学-数学

CiteScore

3.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years. An eminent international mathematics journal, the Japanese Journal of Mathematics has been published since 1924. It is an ideal resource for a wide range of mathematicians extending beyond a small circle of specialists. The official journal of the Mathematical Society of Japan. Devoted to authoritative research survey articles that will promote future progress in mathematics. Gives new insight on topics of current interest from broad perspectives and/or reviews all major developments in an important area over many years.