  Polynomials in differentiation operators are considered. The Darboux
transformations covariance determines non-Abelian entries to form the
coefficients of the polynomials. Joint covariance of a pair of such polynomials
(Lax pair) as a function of one-field is studied. Methodically, the transforms
of the coefficients are equalized to Frechet derivatives (first term of the
Taylor series on prolonged space) to establish the operator forms. In the
commutative (Abelian) case that results in binary Bell (Faa de Bruno)
differential polynomials having natural bilinear representation. The example of
generalized Boussinesq equation is studied, the chain equations for the case
are derived. A set of integrable non-commutative potentials and hence nonlinear
equations is constructed altogether with explicit dressing formulas.
