Soliton equations and the zero curvature condition in noncommutative geometry
High Energy Physics - Theory
2016-09-06 v1 Exactly Solvable and Integrable Systems
solv-int
Abstract
Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for GL(1,R) 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 leads to the KP and a modified KP equation. Furthermore, a differential calculus associated with the Boussinesq equation is derived from the KP calculus.
Keywords
Cite
@article{arxiv.hep-th/9608009,
title = {Soliton equations and the zero curvature condition in noncommutative geometry},
author = {A. Dimakis and F. Mueller-Hoissen},
journal= {arXiv preprint arXiv:hep-th/9608009},
year = {2016}
}
Comments
Latex, 10 pages