The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction

Details The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction

2007-10-31

arxiv.org/abs/0710.5820v1

J. Geom. Phys. 60 (2010) 690-707

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, 4 figures

Scientific paper

10.1016/j.geomphys.2010.01.005

The C-quadrilateral lattice (CQL), called also the symmetric lattice, provides geometric interpretation of the discrete CKP equation within the quadrilateral lattice (QL) theory. We discuss affine-geometric properties of the lattice emphasizing the role of the Gallucci theorem in the multidimensional consistency of the CQL. Then we give the algebro-geometric construction of the lattice. We also present the reduction of the vectorial fundamental transformation of the QL to the CQL case. In the Appendix we show a relation between the QL and the so called Darboux maps.

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