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Relation between a Second-Order Spectral Problem and the Confocal Involutive System

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Information Computing and Applications (ICICA 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 244))

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Abstract

The method of nonlinearization of spectral problems has been generalized in various directions and has been applied successfully to many nonlinear partial differential equations. In this paper, a new kind of finite-dimensional completely integrable system related to a second-order spectral problem and the constrained flow of an evolution equations are generated. According to the viewpoint of Hamiltonian mechanics, a reasonable Jacobi-Ostrogradsky coordinate is obtained, and the Lax pairs are nonlinearized. By means of the constrained condition between the potential and the eigenfunctions, the involutive solutions of the evolution equations are given. Moreover, the completely integrability of this system is discussed.

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Author information

Authors and Affiliations

  1. Department of Mathematics & Physics, ShiJiaZhuang TieDao University, 050043, ShiJiaZhuang, China

    Wei Liu & Hai-zhen Sun

  2. Foundation Department, ShiJiaZhuang Vocational College of Finance & Economics, 050061, ShiJiaZhuang, China

    Shan Feng

Authors
  1. Wei Liu
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  2. Hai-zhen Sun
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  3. Shan Feng
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Editor information

Editors and Affiliations

  1. College of Sciences, Hebei United University, 063000, Tangshan, Hebei, China

    Chunfeng Liu

  2. College of Sciences, Hebei United University, Tangshan, 063000, Hebei, China

    Jincai Chang  & Aimin Yang  & 

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© 2011 Springer-Verlag Berlin Heidelberg

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Liu, W., Sun, Hz., Feng, S. (2011). Relation between a Second-Order Spectral Problem and the Confocal Involutive System. In: Liu, C., Chang, J., Yang, A. (eds) Information Computing and Applications. ICICA 2011. Communications in Computer and Information Science, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27452-7_86

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  • DOI: https://doi.org/10.1007/978-3-642-27452-7_86

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27451-0

  • Online ISBN: 978-3-642-27452-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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