A generalized Wadati–Konno–Ichikawa hierarchy and its binary nonlinearization by symmetry constraints Xi-xiang Xu

A generalized Wadati–Konno–Ichikawa hierarchy is derived from a spectral problem. Their Hamiltonian structures are established by means of trace identity. It is shown that the associated hierarchy are all infinite-dimensional integrable systems. Under the binary Bargmann symmetry constraints, the Lax pairs and the adjoint Lax pairs of the resulting hierarchy are all nonlinearized into finite-dimensional completely integrable Hamiltonian systems. An involutive representation of solutions of the resulting hierarchy is given.