  The hierarchy of the integrable nonlinear equations associated with the
quadratic bundle is considered. The expressions for the solution of the
linearization of these equations and their conservation law in the terms of the
solutions of the corresponding Lax pairs are found. It is shown for the first
member of the hierarchy that the conservation law is connected with the
solution of the linearized equation due to the Noether's theorem. The local
hierarchy and three nonlocal ones of the infinitesimal symmetries and the
conservation laws that are explicitly expressed through the variables of the
nonlinear equations are derived.
