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arXiv · 0707.3730

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

A. Tongas·D. Tsoubelis·P. Xenitidis
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Abstract

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 Painlevé equations are considered.

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A. Tongas, D. Tsoubelis, P. Xenitidis. 2007-07-25. Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions. https://doi.org/10.1088/1751-8113%2F40%2F44%2F015

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