scholarly journals The “ghost” symmetry of the BKP hierarchy

2010 ◽  
Vol 51 (5) ◽  
pp. 053514 ◽  
Author(s):  
Jipeng Cheng ◽  
Jingsong He ◽  
Sen Hu
Keyword(s):  
Bkp Hierarchy ◽  
Ghost Symmetry

Some results of the BKP hierarchy as the Kupershmidt reduction of the modified KP hierarchy

2020 ◽  
pp. 2050433
Author(s):  
Yi Yang ◽  
Xiaoli Wang ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Wave Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Bkp Hierarchy

In this paper, the BKP hierarchy is viewed as the Kupershmidt reduction of the modified KP hierarchy. Then based upon this fact, the gauge transformation of the BKP hierarchy are obtained again from the corresponding results of the modified KP hierarchy. Also the constrained BKP hierarchy is constructed from the constrained modified KP hierarchy, and the corresponding gauge transformations are investigated. Particularly, it is found that there is a new kind of gauge transformations generated by the wave functions in the constrained BKP hierarchy.

scholarly journals Constrained lattice-field hierarchies and Toda system with Block symmetry

2016 ◽  
Vol 13 (05) ◽  
pp. 1650061 ◽  
Author(s):  
Chuanzhong Li
Keyword(s):  
Difference Equations ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Lie Symmetry ◽  
Toda System ◽  
One Dimensional ◽  
Toda Hierarchy ◽  
Lattice Field ◽  
The One ◽  
Ghost Symmetry

In this paper, we construct the additional [Formula: see text]-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new integrable difference equations. Under a further reduction, the constrained two-lattice integrable systems can be combined into one single integrable system, namely the well-known one-dimensional original Toda hierarchy. We prove that the one-dimensional original Toda hierarchy has a nice Block Lie symmetry.

A note on the dispersionless BKP hierarchy

2006 ◽  
Vol 39 (24) ◽  
pp. 7641-7655 ◽  
Author(s):  
Yu-Tung Chen ◽  
Ming-Hsien Tu
Keyword(s):  
Bkp Hierarchy

scholarly journals ON THE STRING EQUATION OF THE BKP HIERARCHY

2009 ◽  
Vol 24 (22) ◽  
pp. 4193-4208 ◽  
Author(s):  
HSIN-FU SHEN ◽  
MING-HSIEN TU
Keyword(s):  
Spectral Parameter ◽  
String Equation ◽  
Bkp Hierarchy

The Adler–Shiota–van Moerbeke formula is employed to derive the W-constraints for the p-reduced BKP hierarchy constrained by the string equation. We also provide the Grassmannian description of the string equation in terms of the spectral parameter.

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