A new completely integrable Liouville’s system produced by the Kaup–Newell eigenvalue problem

Source abstract

Under the constraint between the potentials and eigenfunctions, the Kaup–Newell eigenvalue problem is nonlinearized as a new completely integrable Hamiltonian system (R2N,dpΛdq,H): H=i〈Λ2p,q〉+1/2〈Λq,q〉〈Λp,p〉. Furthermore, the involutive solution of the high-order Kaup–Newell equation is obtained. Specifically, the involutive solution of the well-known derivative Schrödinger equation ut=1/2iuxx+1/2(u‖u‖2)x is developed.