Discrete nonlinear hyperbolic equations. Classification of integrable cases
نویسندگان
چکیده
We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on Z2. The fields are associated to the vertices and an equation Q(x1, x2, x3, x4) = 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 three-dimensional cube. This allows to set these equations also on multidimensional lattices Z . We classify integrable equations with complex fields x, and Q affine-linear with respect to all arguments. The method is based on analysis of singular solutions.
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