Abstract
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.