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

Zhuhan Jiang

doi:10.1016/S0375-9601(98)00099-1

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

Zhuhan Jiang

University of New England

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

Differential-difference equations (DDEs) u^(k)_n (t) = F_n(t,U_n+a,...,U_n+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.

Original language	English
Pages (from-to)	137-143
Number of pages	7
Journal	Physics Letters. Section A: General, Atomic and Solid State Physics
Volume	240
Issue number	3
DOIs	https://doi.org/10.1016/S0375-9601(98)00099-1
Publication status	Published - 30 Mar 1998
Externally published	Yes

Keywords

Differential-difference equations
Integrability
Lie point symmetries

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10.1016/S0375-9601(98)00099-1

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AB - Differential-difference equations (DDEs) u(k)n (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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KW - Integrability

KW - Lie point symmetries

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

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Keywords

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