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

Abstract

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.

arXiv comment10 pages

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• A new approach to deformation equations of noncommutative KP hierarchies
• Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations
• Bidifferential graded algebras and integrable systems
• Quasideterminant solutions of NC Painlevé II equation with the Toda solution at $n=1$ as a seed solution in its Darboux transformation
• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
• Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System