数学物理学报(英文版) ›› 1993, Vol. 13 ›› Issue (4): 449-456.
李忠定
Li Zhongding
摘要: Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T=(-<A2q, q>, <A2p, p>)T=f(q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp∧dq, H=H1) with the Hamiltonian
H1=-<A3q,p>-(1/2)<A2p,p><A2q,q>.
while the nonlinearization of the time part leads to its N-involutive system {Hm}. The involutive solution of the compatible fsystem (H1), (Hm) is mapped by into the solution of the higher order Kaup-Newell equation.