Integrable mappings for noncommuting objects
Andrei N. Leznov, Emil A. Yuzbashyan
TL;DR
This paper develops hierarchies of integrable systems for noncommuting objects, extending the Darboux-Toda mapping approach to noncommutative and Grassmann-variable cases, broadening the scope of integrable mappings.
Contribution
It introduces a novel framework for integrable mappings involving noncommutative objects and Grassmann variables, generalizing classical integrable system approaches.
Findings
Hierarchies of integrable systems for noncommutative objects constructed.
Extension of integrable mappings to Grassmann-variable dependent functions.
Generalization of the Darboux-Toda mapping to noncommutative settings.
Abstract
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems. Besides the usual setup with one time and two space dimensions, we consider the case when the unknown functions also depend on two Grassman variables.
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