Integrable non-commutative equations on quad-graphs. The consistency approach

Details Integrable non-commutative equations on quad-graphs. The consistency approach Integrable non-commutative equations on quad-graphs. The consistency approach

2002-06-10

arxiv.org/abs/nlin/0206010v1

Lett. Math. Phys., 2002, vol. 61, p. 241-254

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX2e, 16 pp

Scientific paper

We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the three-dimensional consistency property remains valid in this case. We derive the non-commutative zero curvature representations for these systems, based on the latter property. Quantum systems with their quantum zero curvature representations are particular cases of the general non-commutative ones.

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