2017
DOI: 10.3842/sigma.2017.051
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Self-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice

Abstract: Abstract. We recently introduced a class of Z N graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduced a subclass, which we called "self-dual". In this paper we discuss the continuous symmetries of these systems, their reductions and the relation of the latter to the Bogoyavlensky equation.

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Cited by 2 publications
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“…This leaves a plethora of other degenerate cases, which we believe to be a rich source of low dimensional reductions. We comment that another Bogoyavlenskii lattice arises in the context of symmetries of the self-dual generic system for N = 3 [15]. For N > 3, the corresponding systems give rise to multi-component generalisations of the Bogoyavlenskii lattice.…”
Section: Conclusion and Discussionmentioning
confidence: 92%
“…This leaves a plethora of other degenerate cases, which we believe to be a rich source of low dimensional reductions. We comment that another Bogoyavlenskii lattice arises in the context of symmetries of the self-dual generic system for N = 3 [15]. For N > 3, the corresponding systems give rise to multi-component generalisations of the Bogoyavlenskii lattice.…”
Section: Conclusion and Discussionmentioning
confidence: 92%