A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems (Q2737918)

The authors introduce an isospectral problem and study the associated hierarchy of nonlinear evolution equations. This hierarchy possesses bi--Hamiltonian structure, so, by a theorem of Magri, it is integrable in Liouville's sense. As an example, a new generalized Schrödinger equation is obtained. The eigenvalue problem can be nonlinearized as a finite--dimensional completely integrable system under the Bergmann constraint between the potentials and the eigenvalues.