A hierarchy of non-linear evolution equations its Hamiltonian structure and classical integrable system

@inproceedings{Xianguo1992AHO,
  title={A hierarchy of non-linear evolution equations its Hamiltonian structure and classical integrable system},
  author={Geng Xianguo},
  year={1992}
}
An isospectral problem and a new corresponding hierarchy of non-linear evolution equations are proposed. As a reduction, a new generalized non-linear Schrodinger equation is obtained. It is shown that the hierarchy of equations possesses a bi-Hamiltonian structure. The eigenvalue problem is non-linearized so as to be a finite-dimensional completely integrable system under a constraint between the potentials and the eigenfunctions.