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Symmetry Groups of Differential Equations

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

Abstract

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.

Keywords

Group Action Symmetry Group Recursion Relation Infinitesimal Generator Invariant Solution 
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

© 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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