  We present a detailed analysis of the structure of the conservation laws in
quantum integrable chains of the XYZ-type and in the Hubbard model. With the
use of the boost operator, we establish the general form of the XYZ conserved
charges in terms of simple polynomials in spin variables and derive recursion
relations for the relative coefficients of these polynomials. For two submodels
of the XYZ chain - namely the XXX and XY cases, all the charges can be
calculated in closed form. For the XXX case, a simple description of conserved
charges is found in terms of a Catalan tree. This construction is generalized
for the su(M) invariant integrable chain. We also indicate that a quantum
recursive (ladder) operator can be traced back to the presence of a hamiltonian
mastersymmetry of degree one in the classical continuous version of the model.
We show that in the quantum continuous limits of the XYZ model, the ladder
property of the boost operator disappears. For the Hubbard model we demonstrate
the non-existence of a ladder operator. Nevertheless, the general structure of
the conserved charges is indicated, and the expression for the terms linear in
the model's free parameter for all charges is derived in closed form.
