Discrete nonlinear hyperbolic equations. Classification of integrable cases
Abstract
We consider discrete nonlinear hyperbolic equations on quadgraphs, in particular on the square lattice. The fields are associated to the vertices and an equation Q(x_1,x_2,x_3,x_4)=0 relates four fields at one quad. Integrability of equations is understood as 3Dconsistency. The latter is a possibility to consistently impose equations of the same type on all the faces of a threedimensional cube. This allows to set these equations also on multidimensional lattices Z^N. We classify integrable equations with complex fields x, and Q affinelinear with respect to all arguments. The method is based on analysis of singular solutions.
 Publication:

arXiv eprints
 Pub Date:
 May 2007
 arXiv:
 arXiv:0705.1663
 Bibcode:
 2007arXiv0705.1663A
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 19 pages