Lax representation and Bäcklund-Darboux transformation for coupled BKP hierarchy

被引：0

作者：

Duan, Xiaojuan ^{[1
]}

Cheng, Jipeng ^{[2
,3
]}

机构：

[1] Xiamen Univ Technol, Sch Math & Stat, Xiamen 361024, Peoples R China

[2] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China

[3] Jiangsu Ctr Appl Math CUMT, Xuzhou 221116, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2024年 / 65卷 / 05期

基金：

中国国家自然科学基金;

关键词：

INTEGRABLE HIERARCHIES;

D O I：

10.1063/5.0206537

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

By using vertex operator representation of polynomial Lie algebra b(infinity)((n)), a theoretical interpretation of coupled BKP hierarchy is given, where corresponding Hirota bilinear equations are derived. Then based upon this, a wave function matrix is introduced, so that we can construct the corresponding dressing operator matrix and obtain the coupled BKP constraints and Sato equation, which allows us to define the Lax operator matrix and obtain the Lax equation. It is found that the coupled BKP hierarchy is a special case of matrix KP theory. Lastly, we present the B & auml;cklund-Darboux transformations for the coupled BKP equations from both fermionic and bosonic pictures.

引用

页数：12