On an extension of the generalized BGW tau-function

For an arbitrary solution to the Burgers–KdV hierarchy, we define tau-tuple $$(\tau _1,\tau _2)$$ of solution. We show that product $$\tau _1\tau _2$$ admits Buryak’s residue formula. Therefore, according Alexandrov’s theorem, is a tau-function KP hierarchy. then derive formula for affine coordinates point Sato Grassmannian corresponding explicitly in terms those _1$$ . Applications analogous open extension generalized BGW and partition function are given.