  Using the algebraic method of Gardner's deformations for completely
integrable systems, we construct the recurrence relations for densities of the
Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending
the Magri schemes for these systems, we obtain new integrable equations adjoint
with respect to the initial ones and describe their Hamiltonian structures and
symmetry properties.

Exactly Solvable and Integrable Systems;Pattern Formation and Solitons