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arXiv · 1801.00589

Differential Calculi on Associative Algebras and Integrable Systems

Aristophanes Dimakis·Folkert Müller-Hoissen
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Abstract

After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from it. We also recall a matrix version of the binary Darboux transformation and, inspired by the so-called Cauchy matrix approach, present an infinite system of equations solved by it. Finally, we sketch recent work on a deformation of the matrix binary Darboux transformation in bidifferential calculus, leading to a treatment of integrable equations with sources.

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Aristophanes Dimakis, Folkert Müller-Hoissen. 2018-01-02. Differential Calculi on Associative Algebras and Integrable Systems. https://arxiv.org/abs/1801.00589

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