Symmetry Groups of Differential Equations
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.
KeywordsGroup Action Symmetry Group Recursion Relation Infinitesimal Generator Invariant Solution
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