数学物理学报(英文版) ›› 1990, Vol. 10 ›› Issue (3): 241-249.

• 论文 •    下一篇

THE CONFOCAL INVOLUTIVE SYSTEM AND THE INTEGRABILITY OF THE NONLINEARIZED LAX SYSTEMS FOR AKNS HIERARCHY

马文秀   

  1. Computing Center, Academia Sinica, Beijing, China
  • 收稿日期:1989-05-15 出版日期:1990-09-25 发布日期:1990-09-25

THE CONFOCAL INVOLUTIVE SYSTEM AND THE INTEGRABILITY OF THE NONLINEARIZED LAX SYSTEMS FOR AKNS HIERARCHY

Ma Wenxiu   

  1. Computing Center, Academia Sinica, Beijing, China
  • Received:1989-05-15 Online:1990-09-25 Published:1990-09-25

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摘要： The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n ≤ 3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.

Abstract: The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n ≤ 3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.

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