New Finite-Dimensional Integrable Systems by Binary Nonlinearization of WKI Equations

A symmetry constraint for Wadati-Konno-Ichikawa (WKI) equations is presented by binary nonlinearization. The spatial part and the temporal parts of Lax pairs and the adjointt Lax pairs of WKI equations are all constrainted as finite dimensional Liouville integrable Hamiltonian systems, whose integrals of motion are explicitly given.