Theoretical and Mathematical Physics

, Volume 110, Issue 3, pp 267–276 | Cite as

On some generalizations of the factorization method

  • I. Z. Golubchik
  • V. V. Sokolov


The classical factorization method reduces the study of a system of ordinary differential equations Ut=[U+, U] to solving algebraic equations. Here U(t) belongs to a Lie algebra\(\mathfrak{G}\) which is the direct sum of its subalgebras\(\mathfrak{G}_ + \) and\(\mathfrak{G}_ - \), where “+” signifies the projection on\(\mathfrak{G}_ + \). We generalize this method to the case\(\mathfrak{G}_ + \cap \mathfrak{G}_ - \ne \{ 0\} \). The corresponding quadratic systems are reducible to a linear system with variable coefficients. It is shown that the generalized version of the factorization method can also be applied to Liouville equation-type systems of partial differential equations.


Soliton Variable Coefficient Factorization Method Logarithmic Derivative Triangular Matrice 
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  1. 1.
    B. Kostant, “Quantization and representation theory,” in:Lect. Notes, Vol. 34 (1979), pp. 287–316.Google Scholar
  2. 2.
    M. A. Semenov-Tyan-Shanskii,Funkts. Anal. Prilozhen.,17, No. 4, 17–33 (1983).MathSciNetGoogle Scholar
  3. 3.
    L. A. Takhtadzhyan and L. D. Faddeev,Hamiltonian Approach in the Theory of Solitons, Springer, Berlin-Heidelberg-New York (1986).Google Scholar
  4. 4.
    I. Z. Golubchik, V. V. Sokolov, and S. I. Svinolupov, “A new class of nonassociative algebras and a generalized factorization method,” Preprint No. 53, E. Schrödinger Inst., Wien (1993).Google Scholar
  5. 5.
    O. I. Bogoyavlenskii,Breaking Solitons [in Russian], Nauka, Moscow (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • I. Z. Golubchik
    • 1
  • V. V. Sokolov
    • 1
  1. 1.Mathematical Institute, Ufa Scientific CenterRussian Academy of SciencesUSSR

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