A Matrix Integral Solution to [ P , Q ] = P and Matrix Laplace Transforms

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q] = P , where P flows according to the KP hierarchy ∂P/∂tn = [(P )+, P ], with p := ordP ≥ 2; (ii) find a matrix integral representation for the associated τ -function. First we construct an infinite dimensional space W = spanC { ψ0(z), ψ1(z… CONTINUE READING