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From the Kadomtsev-Petviashvili equation halfway to Ward's chiral model
Aristophanes Dimakis, Folkert Muller-Hoissen
The "pseudodual" of Ward's modified chiral model is a dispersionless limit of the matrix Kadomtsev-Petviashvili (KP) equation. This relation allows to carry solution techniques fro…
Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
Aristophanes Dimakis, Folkert Muller-Hoissen
The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the…
A new approach to deformation equations of noncommutative KP hierarchies
Aristophanes Dimakis, Folkert Muller-Hoissen
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matri…
Weakly nonassociative algebras, Riccati and KP hierarchies
Aristophanes Dimakis, Folkert Muller-Hoissen
It has recently been observed that certain nonassociative algebras (called "weakly nonassociative", WNA) determine, via a universal hierarchy of ordinary differential equations, so…