Journal of Physics A Mathematical and General · 2006 · 16 citations · 20 references
Natural SciencesMathematicsDifferential EquationsDifference EquationsIntegrable SystemsPartial Differential EquationsConservation LawsDifference Equation ModelsHigher-order Difference EquationsIntegrable Partial Differential EquationsIntegrodifference EquationsNonlinear Difference EquationsQ-difference Equations
This paper presents a classification of all three-point conservation laws for a large class of integrable difference equations that has been described by Nijhoff, Quispel and Capel. We show that every nonlinear equation from this class has at least two nontrivial conservation laws. Most of the conservation laws that are found are new.
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Applications of lie groups to differential equations
Acta Applicandae Mathematicae · 1990 · 6.1K citations
Do integrable mappings have the Painlevé property?
B. Grammaticos, A. Ramani, V. Papageorgiou · Physical Review Letters · 1991 · 483 citations