On zero-curvature representations of evolution equations

For zero-curvature representations (ZCRs) At-Bx-AB+BA=0 of evolution equations ut=f(x, u, ux, ..., ux...x), we develop a description which is invariant under gauge transformations A'=SAS-1-SxS-1 and B'=SBS-1-StS-1, where A, B and S are matrix functions of x, u, ux, uxx, ... . We prove that every fixed matrix A of any dimension and order (in ux...x) determines a continual class of evolution equations which admit ZCRs with this A. Then we quote examples illustrating how a dependence of A on an essential parameter restricts classes of represented equations. One of our examples shows that some non-integrable systems can admit parametric Lax pairs and infinitely many non-trivial conservation laws.