Classical Darboux transformations and the KP hierarchy

2001 ◽  
Vol 17 (4) ◽  
pp. 1067-1074 ◽  
Author(s):  
F Lambert ◽  
I Loris ◽  
J Springael
Keyword(s):  
Darboux Transformations ◽  
Kp Hierarchy

Darboux transformations and Darboux coverings: some applications to the KP hierarchy

1998 ◽  
Vol 15 (4) ◽  
Author(s):  
Paolo Casati ◽  
GREGORIO Falqui ◽  
FRANCO Magri ◽  
Marco Pedroni ◽  
Jorge Zubelli
Keyword(s):  
Darboux Transformations ◽  
Kp Hierarchy

scholarly journals Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting

2001 ◽  
Vol 53 (2) ◽  
pp. 278-309 ◽  
Author(s):  
G. F. Helminck ◽  
J. W. van de Leur
Keyword(s):  
Closed Form ◽  
Darboux Transformations ◽  
Kp Hierarchy ◽  
Geometric Data

AbstractIn this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the KP hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of τ-functions is given.

Darboux transformations for the strict KP hierarchy

2021 ◽  
Vol 206 (3) ◽  
pp. 296-314
Author(s):  
G. F. Helminck ◽  
E. A. Panasenko
Keyword(s):  
Darboux Transformations ◽  
Kp Hierarchy ◽  
Strict Kp Hierarchy

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

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