
SIGMA 13 (2017), 051, 10 pages arXiv:1705.00518
https://doi.org/10.3842/SIGMA.2017.051
Contribution to the Special Issue on Symmetries and Integrability of Difference Equations
SelfDual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice
Allan P. Fordy ^{a} and Pavlos Xenitidis ^{b}
^{a)} School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
^{b)} School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7FS, UK
Received May 01, 2017, in final form June 26, 2017; Published online July 06, 2017
Abstract
We recently introduced a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduced a subclass, which we called ''selfdual''. In this paper we discuss the continuous symmetries of these systems, their reductions and the relation of the latter to the Bogoyavlensky equation.
Key words:
discrete integrable system; Lax pair; symmetry; Bogoyavlensky system.
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References

Bogoyavlensky O.I., Integrable discretizations of the KdV equation, Phys. Lett. A 134 (1988), 3438.

Fordy A.P., Xenitidis P., $\mathbb{Z}_N$ graded discrete Lax pairs and discrete integrable systems, arXiv:1411.6059.

Fordy A.P., Xenitidis P., ${\mathbb Z}_N$ graded discrete Lax pairs and integrable difference equations, J. Phys. A: Math. Theor. 50 (2017), 165205, 30 pages.

Marì Beffa G., Wang J.P., Hamiltonian evolutions of twisted polygons in ${\mathbb{RP}}^n$, Nonlinearity 26 (2013), 25152551, arXiv:1207.6524.

Mikhailov A.V., Xenitidis P., Second order integrability conditions for difference equations: an integrable equation, Lett. Math. Phys. 104 (2014), 431450, arXiv:1305.4347.

Yamilov R., Symmetries as integrability criteria for differential difference equations, J. Phys. A: Math. Gen. 39 (2006), R541R623.

