Backlund problem,differential algebra and group theory

  • Jean-François Pommaret
Session II — Completely Integrable Systems and Group Theory
Part of the Lecture Notes in Physics book series (LNP, volume 180)


Our purpose is to prove that certain concepts of mathematical physics involving partial differential equations (PDE) can only be clearly understood in the framework of a new branch of mathematics called “differential algebraic geometry”.By this way, we give a new setting for the inverse Bäcklund problem and relate it to the differential Galois theory.


GALOIS Theory Galois Extension Partial Differential Equation Differential Algebra Differential Ideal 


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  1. 1).
    E.GOURSAT:Le problème de Bäcklund,Mémorial des Sciences Mathématiques,n°6,Gauthier-Villars,1925,53p.Google Scholar
  2. 2).
    J.F.POMMARET:Systems of partial differential equations and Lie pseudogroups,Gordon and Breach,1978,426p.Google Scholar
  3. 3).
    J.F.POMMARET:Differential Galois theory,Gordon and Breach, 1982,760p.Google Scholar
  4. 4).
    E:VESSIOT:Sur la théorie de Galois et ses diverses généra-lisations, Ann.Sc.Ec.Norm.Sup.,21,1904,p.9.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Jean-François Pommaret
    • 1
  1. 1.Département de MathématiquesEcole Nationale des Ponts et ChausséesParisFrance

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