Reduced 4th-Order Eigenvalue Problem

  • Shu-hong Wang
  • Bao-cai Zhang
  • Zhu-quan Gu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7030)


The technique of the so-called nonlinearization of Lax pairs has been developed and applied to various soliton hierarchies, and this method also was generalized to discuss the nonlinearization of Lax pairs and adjoint Lax pairs of soliton hierarchies. In this paper, by use of the nonlinearization method, the reduced 4th-order eigenvalue problem is discussed and a Lax representation was deduced for the system. By means of Euler-Lagrange equations and Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system has been found, and the Bargmann system have been given. Then, the infinite-dimensional motion system described by Lagrange mechaics is changed into the Hamilton cannonical coordinate system.


Eigenvalue problem Reduced System Jacobi-Ostrogradsky coordinate Bargmann system 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shu-hong Wang
    • 1
  • Bao-cai Zhang
    • 2
  • Zhu-quan Gu
    • 2
  1. 1.College of MathematicsInner Mongolia University for NationalitiesTongliaoChina
  2. 2.Department of Mathematics and PhysisShijiazhuang Tiedao UniversityShijiazhuangChina

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