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There are well-known constructions of integrable systems that arechains of infinitely many copies of the equations of the KPhierarchy “glued” together with some additional variables, forexample, the modified KP hierarchy. Another interpretation of thelatter, in terms of infinite matrices, is called the 1-Todalattice hierarchy. One way infinite reduction of this hierarchyhas all the solutions in the form of sequences of expandingWronskians. We define another chain of the KP equations, alsowith solutions of the Wronsksian type, that is characterized bythe property to stabilize with respect to a gradation. Under someconstraints imposed, the tau functions of the chain are the taufunctions associated with the Kontsevich integrals

journal of applied mathematics

Chains of KP, semi-infinite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn></mml:math>-Toda lattice hierarchy and Kontsevich integral

Chains of KP, semi-infinite1-Toda lattice hierarchy and Kontsevich integral