Affine linear and D 4 symmetric lattice equations: symmetry analysis and reductions
2007; Institute of Physics; Volume: 40; Issue: 44 Linguagem: Inglês
10.1088/1751-8113/40/44/015
ISSN1751-8121
AutoresAnastasios Tongas, D. Tsoubelis, Pavlos Xenitidis,
Tópico(s)Molecular spectroscopy and chirality
ResumoWe 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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