大型 BKP 层次结构的松弛结构和 tau 函数

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Wenchuang Guan, Shen Wang, Wenjuan Rui, Jipeng Cheng
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引用次数: 0

摘要

本文主要研究大 BKP 层次(又称 B 型托达层次)的 Lax 结构和 tau 函数。首先,大 BKP 层次可以通过特殊的玻色子化从费米子 BKP 层次推导出来,并以双线性方程的形式呈现。然后从双线性方程出发,给出相应的拉克斯方程,特别是流发生器与拉克斯算子的关系。同时,从 Lax 方程出发,讨论了相应的双线性方程和 tau 函数的存在性。之后,大 BKP 层次结构被视为修正托达(mToda)层次结构的子层次结构,也称为双分量第一修正 KP 层次结构。最后,通过使用从 mToda 到 Toda 的两个基本 Miura 变换,我们理解了 large BKP tau 函数 (\tau _n(\textbf{t})\)和 Toda tau 函数 (\tau _n^\textrm{Toda}(\textbf{t}、-textbf{t})),也就是说,(\tau _n^{textrm{Toda}}(\textbf{t}、-{textbf{t}})=\tau _n(\textbf{t})\tau _{n-1}(\textbf{t})\),并且(\tau _n^{textrm{Toda}}(\textbf{t},-{\textbf{t}})=\tau _n^2(\textbf{t})\)。进一步,我们发现 \(\big (\tau _n(\textbf{t})\tau _{n-1}(\textbf{t}),\tau _n^2(\textbf{t})\big )\) 满足 mToda 层次的双线性方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lax structure and tau function for large BKP hierarchy

In this paper, we mainly investigate Lax structure and tau function for the large BKP hierarchy, which is also known as Toda hierarchy of B type. Firstly, the large BKP hierarchy can be derived from fermionic BKP hierarchy by using a special bosonization, which is presented in the form of bilinear equation. Then from bilinear equation, the corresponding Lax equation is given, where in particular the relation of flow generator with Lax operator is obtained. Also starting from Lax equation, the corresponding bilinear equation and existence of tau function are discussed. After that, large BKP hierarchy is viewed as sub-hierarchy of modified Toda (mToda) hierarchy, also called two-component first modified KP hierarchy. Finally by using two basic Miura transformations from mToda to Toda, we understand two typical relations between large BKP tau function \(\tau _n(\textbf{t})\) and Toda tau function \(\tau _n^\textrm{Toda}(\textbf{t},-\textbf{t})\), that is, \(\tau _n^{\textrm{Toda}}(\textbf{t},-{\textbf{t}})=\tau _n(\textbf{t})\tau _{n-1}(\textbf{t})\) and \(\tau _n^{\textrm{Toda}}(\textbf{t},-{\textbf{t}})=\tau _n^2(\textbf{t})\). Further, we find \(\big (\tau _n(\textbf{t})\tau _{n-1}(\textbf{t}),\tau _n^2(\textbf{t})\big )\) satisfies bilinear equation of mToda hierarchy.

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来源期刊
Letters in Mathematical Physics
Letters in Mathematical Physics 物理-物理:数学物理
CiteScore
2.40
自引率
8.30%
发文量
111
审稿时长
3 months
期刊介绍: The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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