New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations

Abstract

Through taking a Bargmann symmetry constraint, the spectral problem and the adjoint spectral problem of KdV integrable hierarchy are transformed into a finite dimensional integrable Hamiltonian system in the Liouville sense. Meantime, under the control of this system (i.e. the spatial part), the time parts of the constrained Lax pairs and adjoint Lax pairs are reduced to a new hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, whose Hamiltonian functions constitute a series of integrals of motion for the spatial part of the constrained Lax pairs and adjoint Lax pairs.