Sato's Bäcklund transformations, additional symmetries and ASvM formula for the discrete KP hierarchy

2010 ◽  
Vol 43 (13) ◽  
pp. 135202 ◽  
Author(s):  
Liu Shaowei ◽  
Cheng Yi
Keyword(s):  
Bäcklund Transformations ◽  
Kp Hierarchy ◽  
Additional Symmetries ◽  
Backlund Transformations ◽  
Discrete Kp Hierarchy ◽  
Discrete Kp

Sato–Bäcklund transformations and string equations of the mKP hierarchy

2019 ◽  
Vol 34 (25) ◽  
pp. 1950142 ◽  
Author(s):  
Huizhan Chen ◽  
Lumin Geng ◽  
Jipeng Cheng
Keyword(s):  
Bäcklund Transformations ◽  
Kp Hierarchy ◽  
Time And Space ◽  
Additional Symmetry ◽  
Tau Functions ◽  
Virasoro Constraint ◽  
Backlund Transformations ◽  
Lax Operator ◽  
Important Kind

Additional symmetry is an important kind of symmetries depending explicitly on the time and space variables, which can be expressed through Sato–Bäcklund transformations. In this paper, we construct Sato–Bäcklund transformations of the modified KP hierarchy and its constrained cases. Then the string equations of the [Formula: see text]-reduced modified KP hierarchy are established by requiring the system independent on some additional symmetry flows, which are expressed by the Lax operator [Formula: see text] and the Orlov–Shulman’s operator [Formula: see text]. At last, we obtain the negative Virasoro constraint on the two tau functions of the 2-reduced modified KP hierarchy satisfying the string equations.

Casorati and Discrete Gram Type Determinant Representations of Solutions to the Discrete KP Hierarchy

1993 ◽  
Vol 62 (6) ◽  
pp. 1872-1886 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Ryogo Hirota ◽  
Satoshi Tsujimoto ◽  
Tatsuya Imai
Keyword(s):  
Kp Hierarchy ◽  
Discrete Kp Hierarchy ◽  
Discrete Kp
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