$s$-次推广的超 KP 可积系列: 从一分量到多分量

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1602-1615.

$s$-次推广的超 KP 可积系列: 从一分量到多分量

陈慧展()

中国矿业大学数学学院江苏徐州 221116

收稿日期:2024-10-18 修回日期:2025-04-14 出版日期:2025-10-26 发布日期:2025-10-14
作者简介:陈慧展, E-mail:chenhuizhan@cumt.edu.cn
基金资助:
中央高校基本科研业务费(JSX250005)

The $s$-th Generalized Super KP Hierarchy: From One Component to Multi-Components

Huizhan Chen()

School of Mathematics, China University of Mining and Technology, Jiangsu Xuzhou 221116

Received:2024-10-18 Revised:2025-04-14 Online:2025-10-26 Published:2025-10-14
Supported by:
Fundamental Research Funds for the Central Universities(JSX250005)

摘要/Abstract

摘要：

该文考虑了 Kac-van de Leur 版本下超 KP 可积系列的一类推广系统, 即 $s$-次推广的超 KP 可积系列. 首先, 利用克利福德超代数与 A 型无穷维李超代数给出该系统在超费米 Fock 空间中的定义, 其表现形式是一个用 $\tau$ 函数表达的恒等式. 其次, 利用 A 型超玻色-费米对应给出 $s$-次推广的超 KP 可积系列在超玻色 Fock 空间中的像, 即一个含有超变量的偏微分方程系统. 在此基础上, 给出该系统的超 Hirota 双线性形式, 并从中导出 KP 方程和超 KP 方程. 最后, 该系统被推广到多分量情形.

关键词: $s$-次推广的超 KP 可积系列, 无穷维李超代数, A 型超玻色-费米对应, KP 方程, 超 KP 方程

Abstract:

In this paper, a generalized system of the super KP hierarchy of Kac-van de Leur, $s$-th generalized super KP hierarchy, is considered. We characterize the $s$-th generalized super KP hierarchy in super fermionic Fock space using Clifford super algebra and infinite-dimensional Lie superalgebra of type A, which is defined as an identity in terms of tau functions. Using the super boson-fermion correspondence of type A, the image of the $s$-th generalized super KP hierarchy in super bosonic Fock space is given, which is a system of partial differential equations with super variables. Based on this, we give the super Hirota bilinear identity and derive the KP equation and super KP equation from it. Finally, this system is generalized to the multi-component case.

Key words: $s$-th generalized super KP hierarchy, infinite-dimensional Lie superalgebra, super boson-fermion correspondence of type A, KP equation, super KP equation

中图分类号:

O411.1

陈慧展. $s$-次推广的超 KP 可积系列: 从一分量到多分量[J]. 数学物理学报, 2025, 45(5): 1602-1615.

Huizhan Chen. The $s$-th Generalized Super KP Hierarchy: From One Component to Multi-Components[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1602-1615.

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