Symmetry Groups of Differential Equations

  • D. H. Sattinger
  • O. L. Weaver
Part of the Applied Mathematical Sciences book series (AMS, volume 61)


Consider an ordinary differential equation f(x, u, u′) = 0 and assume that the set f(x, u, p) = 0 is a smooth submanifold of ℝ3. A solution of the differential equation is a curve (x, u(x), p(x)) on the surface f = 0 such that p(x) = u′(x). We wish to know what transformations of the x-u plane leave the set of solutions invariant.


Group Action Symmetry Group Recursion Relation Infinitesimal Generator Invariant Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • D. H. Sattinger
    • 1
  • O. L. Weaver
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of PhysicsKansas State UniversityManhattanUSA

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