Elsevier

Physics Letters A

Volume 240, Issue 3, 30 March 1998, Pages 137-143
Physics Letters A

Lie symmetries and their local determinacy for a class of differential-difference equations

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Abstract

Differential-difference equations (DDEs) un(k)(t) = Fn(t, un+a,…, un+b) for k ≥ 2 are studied for their differential Lie symmetries. We observe that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. We also propose 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 given explicitly.

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