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1 January 2002 Chains of KP, semi-infinite $1$-Toda lattice hierarchy and Kontsevich integral
L. A. Dickey
J. Appl. Math. 1(4): 175-193 (1 January 2002). DOI: 10.1155/S1110757X01000122


There are well-known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1-Toda lattice hierarchy. One way infinite reduction of this hierarchy has all the solutions in the form of sequences of expanding Wronskians. We define another chain of the KP equations, also with solutions of the Wronsksian type, that is characterized by the property to stabilize with respect to a gradation. Under some constraints imposed, the tau functions of the chain are the tau functions associated with the Kontsevich integrals.


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L. A. Dickey. "Chains of KP, semi-infinite $1$-Toda lattice hierarchy and Kontsevich integral." J. Appl. Math. 1 (4) 175 - 193, 1 January 2002.


Published: 1 January 2002
First available in Project Euclid: 13 March 2003

zbMATH: 0997.35070
MathSciNet: MR1884975
Digital Object Identifier: 10.1155/S1110757X01000122

Primary: 35Q53 , 35Q58
Secondary: 37K10

Rights: Copyright © 2002 Hindawi

Vol.1 • No. 4 • 1 January 2002
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