Symmetries of Second- and Third-Order Ordinary Differential Equations

  • Fritz Schwarz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2630)


In order to apply Lie’s symmetry theory for solving a differential equation it must be possible to identify the group of symmetries leaving the equation invariant. The answer is obtained in two steps. At first a classification of the possible symmetries of equations of the respective order is determined. Secondly a decision procedure is provided which allows to identify the symmetry type within this classification. For second-order equations the answer has been obtained by Lie himself. In this article the complete answer for quasilinear equations of order three is given. An important tool is the Janet base representation for the determining system of the symmetries.


Base Type Canonical Variable Algebraic Property Determine System Symmetry Class 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Fritz Schwarz
    • 1
  1. 1.FhG, Institut SCAISankt AugustinGermany

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