  We study the heat kernel asymptotics for the Laplace type differential
operators on vector bundles over Riemannian manifolds. In particular this
includes the case of the Laplacians acting on differential p-forms. We extend
our results obtained earlier for the scalar Laplacian and present closed
formulas for all heat invariants associated with these operators. As another
application, we present new explicit formulas for the matrix Korteweg-de Vries
hierarchy.
