# SOLITON EQUATIONS AND THE ZERO CURVATURE CONDITION IN NONCOMMUTATIVE GEOMETRY

@article{Dimakis1996SOLITONEA, title={SOLITON EQUATIONS AND THE ZERO CURVATURE CONDITION IN NONCOMMUTATIVE GEOMETRY}, author={Aristophanes Dimakis and Folkert Mueller-Hoissen}, journal={Journal of Physics A}, year={1996}, volume={29}, pages={7279-7286} }

Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for connections with noncommutative differential calculi. The Burgers equation is formulated in this way and the Cole - Hopf transformation for it attains the interpretation of a transformation of the connection to a pure gauge in this mathematical framework. The KdV, modified KdV equation and the Miura transformation are obtained jointly in a similar setting and a rather straightforward generalization… Expand

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