Symmetry constraint of MKdV equations by binary nonlinearization

A symmetry constraint for MKdV integrable hierarchy is presented by binary nonlinearization. The spatial part and the temporal parts of the Lax pairs and the adjoint Lax pairs of MKdV equations are all constrained as finite dimensional Liouville integrable Hamiltonian systems, whose integrals of motion are explicitly given. In terms of the proposed symmetry constraint, MKdV equations are decomposed into two finite-dimensional Liouville integrable constrained systems and thus a kind of separation of variables for MKdV equations is established.