415 citations
- National Technical University of AthensGR169 papers
- National and Kapodistrian University of AthensGR159 papers
- European Organization for Nuclear ResearchCH158 papers
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11 papers · 1 filter
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
Aristophanes Dimakis, Folkert Müller-Hoissen
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-t…
On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system
Takayuki Tsuchida, Aristophanes Dimakis
We propose a natural (2+1)-dimensional generalization of the Ablowitz-Ladik lattice that is an integrable space discretization of the cubic nonlinear Schroedinger (NLS) system in 1…
Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
Aristophanes Dimakis, Folkert Mueller-Hoissen
We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this…
Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System
Aristophanes Dimakis, Folkert Müller-Hoissen
Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also sol…
Bidifferential graded algebras and integrable systems
Aristophanes Dimakis, Folkert Muller-Hoissen
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
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…