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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
Article

Abstract

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.

Keywords

Soliton Variable Coefficient Factorization Method Logarithmic Derivative Triangular Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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