Abstract
In the case of the KP hierarchy where the dependent variable takes values in an (arbitrary) associative algebra , 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 ) and by use of a Cole–Hopf transformation. For this class of exact solutions we work out a correspondence with ‘weakly nonassociative’ algebras.
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