Generalized Kaup-Newell spectral problem, soliton equations and finite-dimensional integrable systems

A generalized Kaup-Newell spectral problem is introduced. This spectral problem corresponds to infinitely many hierarchies of soliton equations. Further two reductions of the generalized Kaup-Newell spectral problem are discussed and two new hierarchies of associated soliton equations are derived. Through non-linearization of two reductive spectral problems, two new finite-dimensional integrable systems are engendered, which possess non-confocal involutive integrals of motion