Zero Curvature Conditions on W _∞, Trigonometrical and Universal Enveloping Algebras

Abstract

The use of first order differential operators

(14.1)

in the construction of non-linear evolution equations posessing an infinite number of conserved quantities involved a finite number of x and t dependent fields q _{r s} (x, t) (r, s = 1 ... N), that made up Q. The constant matrix C was chosen diagonal, and the construction of the constants of motion relied on the possibility to ‘diagonalize’ L by means of a similarity transformation R, which required the solution of certain recursion relations, (13.5).