Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions

Details Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions

2007-07-25

arxiv.org/abs/0707.3730v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

31 pages

Scientific paper

10.1088/1751-8113/40/44/015

We consider lattice equations on ${\mathds{Z}}^2$ which are autonomous, affine linear and possess the symmetries of the square. Some basic properties of equations of this type are derived, as well as a sufficient linearization condition and a conservation law. A systematic analysis of the Lie point and the generalized three- and five-point symmetries is presented. It leads to the generic form of the symmetry generators of all the equations in this class, which satisfy a certain non-degeneracy condition. Finally, symmetry reductions of certain lattice equations to discrete analogues of the Painlev\'e equations are considered.

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