Soliton equations and the zero curvature condition in noncommutative geometry

Details Soliton equations and the zero curvature condition in noncommutative geometry Soliton equations and the zero curvature condition in noncommutative geometry

1996-08-01

arxiv.org/abs/hep-th/9608009v1

J.Phys.A29:7279-7286,1996

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 10 pages

Scientific paper

10.1088/0305-4470/29/22/022

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.

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