Gauge Transformations and Weak Lax Equation
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
We consider several integrable systems from a standpoint of the SL(2,R) invariant gauge theory. In the Drinfeld-Sokorov gauge, we get a one parameter family of nonlinear equations from zero curvature conditions. For each value of the parameter the equation is described by weak Lax equations. It is transformed to a set of coupled equations which pass the Painlev\'{e} test and are integrable for any integer values of the parameter. Performing successive gauge transformations (the Miura transformations) on the system of equations we obtain a series of nonlinear equations.
Cite
@article{arxiv.nlin/0108043,
title = {Gauge Transformations and Weak Lax Equation},
author = {Takeshi Fukuyama and Kiyoshi Kamimura and Kouichi Toda},
journal= {arXiv preprint arXiv:nlin/0108043},
year = {2007}
}
Comments
16 pages