English

The Generalised mKdV Equations for Level -3 of $\hat{sl}_2$

solv-int 2007-05-23 v1 Exactly Solvable and Integrable Systems

Abstract

A certain generalisation of the hierarchy of mKdV equations (modified KdV), which forms an integrable system, is studied here. This generalisation is based on a Lax operator associated to the equations, with principal components of degrees between -3 and 0. The results are the following ones: 1) an isomorphism between the space of jets of the system and a quotient of Sl2(\CC((t))){Sl}_2({\CC}((t))); 2) the fact that the monodromy matrixes of the Lax operators have, morover, Poisson brackets given by the trigonometric r-matrix; 3) a definition of the action of screening operators on the densities; 4) an identification of the intersection of the kernel with the integrals of motion.

Keywords

Cite

@article{arxiv.solv-int/9809011,
  title  = {The Generalised mKdV Equations for Level -3 of $\hat{sl}_2$},
  author = {A. Balan},
  journal= {arXiv preprint arXiv:solv-int/9809011},
  year   = {2007}
}