数学物理学报(英文版) ›› 1993, Vol. 13 ›› Issue (4): 449-456.

• 论文 • 上一篇    下一篇

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

李忠定   

  1. Shijiazhuan Railway Institute, Shijiazhuang 050043, China
  • 收稿日期:1989-11-12 出版日期:1993-12-25 发布日期:1993-12-25

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

Li Zhongding   

  1. Shijiazhuan Railway Institute, Shijiazhuang 050043, China
  • Received:1989-11-12 Online:1993-12-25 Published:1993-12-25

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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.

Abstract: 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.

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