HOW TO CONSTRUCT LAX REPRESENTATIONFOR CONSTRAINED FLOWS OF THE BOUSSINESQ HIERARCHY VIA ADJOINT REPRESENTATIONS

By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A method to construct the Lax representations for both x- and tn- constrained flows via reduction of the adjoint representations of the auxiliary linear problems is developed.