EQUATION OF MATHEMATICAL PHYSICS AND OTHER AREAS OF APPLICATION: A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL EQUATION

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 HamiltonianH1+-Aq,p-（1/2）A2p,pA2q,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.