Comments on Some Algebraic Properties of the Gauge Equivalent Soliton Equations

Abstract

In references to [1], [2], a theory is proposed for generating the constants of motion, the symmetries and their Lie algebra for some dynamical systems, where three parameters α, β are introduced. In this paper, we have proved that if the soliton equations in dynamical systems are gauge equivalent, then the parameters α, β, h are invariant and the Lie algebra of the symmetries is isomophic under the transformation operator. At last some interesting examples are given.