NEW FINITE-DIMENSIONAL INTEGRABLE SYSTEMS BY SYMMETRY CONSTRAINT OF THE KDV EQUATIONS

Through taking a Bargmann symmetry constraint, the spectral problem an d the adjoint spectral problem of KdV integrable hierarchy are transfo rmed into a finite dimensional integrable Hamiltonian system in the Li ouville sense. Meantime, under the control of this system (i.e. the sp atial part), the time parts of the constrained Lax pairs and adjoint L au pairs are reduced to a new hierarchy of commutative, finite dimensi onal integrable Hamiltonian systems in the Liouville sense, whose Hami ltonian functions constitute a series of integrals of motion for the s patial part of the constrained Lax pairs and adjoint Lax pairs.