A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems

An isospectral problem and the associated hierarchy of nonlinear evolution equations is presented. As a reduction, a new generalized nonlinear Schrodinger equation is obtained. It is shown that the hierarchy possesses bi-Hamiltonian structure and is integrable in Liouville sense. Moreover, the eigenvalue problem can be nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalues. (C) 2000 American Institute of Physics. [S0022-2488(00)00304-2].