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.
Qiao, Zhijun, "A new completely integrable Liouville's system produced by the Kaup-Newell elgenvalue problem" (1993). Mathematical and Statistical Sciences Faculty Publications and Presentations. 13.
Journal of Mathematical Physics