A Full System of Invariants for Third-Order Linear Partial Differential Operators in General Form

  • Ekaterina Shemyakova
  • Franz Winkler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4770)


We find a full system of invariants with respect to gauge transformations Lg − 1 L g for third-order hyperbolic linear partial differential operators on the plane. The operators are considered in a normalized form, in which they have the symbol Sym L  = (pX + qY)XY for some non-zero bivariate functions p and q. For this normalized form, explicit formulae are given. The paper generalizes a previous result for the special, but important, case p = q = 1.


Linear Partial Differential Operators Invariants Gauge transformations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ekaterina Shemyakova
    • 1
  • Franz Winkler
    • 1
  1. 1.Research Institute for Symbolic Computation (RISC), J.Kepler University, Altenbergerstr. 69, A-4040 LinzAustria

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