Gauge Transformations and Weak Lax Equation
Abstract
We consider several integrable systems from a standpoint of the SL(2,R) invariant gauge theory. In the DrinfeldSokorov 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 Painlevé 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:nlin/0108043
 Bibcode:
 2001nlin......8043F
 Keywords:

 Exactly Solvable and Integrable Systems
 EPrint:
 16 pages