Nonlinearization of spectral problems for the perturbation KdV systems

The theory of nonlinearization of spectral problems is developed for invest igating the perturbation KdV systems, and a kind of finite-dimensional inte grable Hamiltonian systems is generated from spectral problems of the pertu rbation KdV systems. To establish the Liouville integrability of the obtain ed Hamiltonian systems, we identify them with the perturbation systems of t he Gamier system, which can be directly proved to be integrable. A useful f ormula to compute the functional gradient of the spectral parameter with re spect to the potential is also presented for arbitrary-order matrix spectra l problems. (C) 2001 Elsevier Science B.V, All rights reserved.