A Liouville integrable Hamiltonian system associated with a generalized Kaup–Newell spectral problem

Starting from a generalized Kaup–Newell spectral problem involving an arbitrary function, we derive a hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as Kaup–Newell equation, Chen–Lee–Liu equation, Gerdjikov–Ivanov equation, Burgers equation, modified Korteweg–de Vries equation and Sharma–Tasso–Olever equation. It is also shown that the hierarchy is integrable in Liouvilleʹs sense and possesses multi-Hamiltonian structure.