A new family of four-dimensional symplectic and integrable mappings

H.W. Capel and R. Sahadevan

Physica A: Statistical Mechanics and its Applications, 2001, vol. 289, issue 1, 86-106

Abstract: We investigate the generalisations of the Quispel, Roberts and Thompson (QRT) family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables. We assume invariance of the rational expression under a cyclic permutation of variables and we impose a symplectic structure with Poisson brackets of the Weyl type. All mappings satisfying these conditions are shown to be integrable either as four-dimensional mappings with two explicit integrals which are in involution with respect to the symplectic structure and which can also be inferred from the periodic reductions of the double-discrete versions of the modified Korteweg–deVries (ΔΔMKdV) and sine-Gordon (ΔΔsG) equations or by reduction to two-dimensional mappings with one integral of the symmetric QRT family.

Keywords: Difference equations; Symplectic and integrable mappings (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:289:y:2001:i:1:p:86-106

DOI: 10.1016/S0378-4371(00)00314-9

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