With a Cole-Hopf transformation to solutions of the noncommutative KP hierarchy in terms of Wronski matrices

In case of the KP hierarchy where the dependent variable takes values in an (arbitrary) associative algebra A, it is known that there are solutions which can be expressed in terms of quasideterminants of a Wronski matrix which solves the linear heat hierarchy. We obtain these solutions without the help of quasideterminants in a simple way via solutions of matrix KP hierarchies (over A) and by use of a Cole-Hopf transformation. For this class of exact solutions we work out a correspondence with ‘weakly nonassociative’ algebras.