1999/10/26 by Yuly Billig, Billig, Yuly
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9910204
23 pages
arxiv created 1999/10/26 · arxiv updated 2009/11/30
The goal of this paper is to give a representation-theoretic interpretation of the sine-Gordon equation. We consider a vertex operator representation of affine Kac-Moody algebra sl2 on the space of differential operators. In this formulation, the tau-function becomes a function of non-commuting variables. Using the skew Casimir operators, we obtain a hierarchy of equations in Hirota form that contains sine-Gordon, KdV and mKdV equations and construct their soliton solutions.