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nlin.SI2012★ 11 cited
Examples of Darboux Integrable Discrete Equations Possessing First Integrals of an Arbitrarily High Minimal Order
Rustem N. Garifullin, Ravil I. Yamilov
We consider a discrete equation, defined on the two-dimensional square lattice, which is linearizable, namely, of the Burgers type and depends on a parameter . For any natural n…
nlin.SI2012★ 1 cited
Affine Lie algebras, Lax pairs and integrable discrete and continuous systems
Rustem N. Garifullin, Ismagil T. Habibullin
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial diffe…
nlin.SI2012★ 40 cited
Generalized symmetry classification of discrete equations of a class depending on twelve parameters
Rustem N. Garifullin, Ravil I. Yamilov
We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result…