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Lie symmetries and their local determinacy for a class of differential-difference equations. (English) Zbl 0946.34056
Summary: Differential-difference equations (DDEs) u n (k) (t)=F n (t,u n+a ,,u n+b ) for k2 are studied for their differential Lie symmetries. The author observes that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. He proposes a mechanism for automating symmetry calculations for fairly general DDEs, with a variety of features exemplified. In particular, the Fermi-Pasta-Ulam system is studied in detail and its new similarity solutions are given explicitly.
34K05General theory of functional-differential equations
34C14Symmetries, invariants (ODE)
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