Discrete nonlinear hyperbolic equations. Classification of integrable cases
By V. E. Adler, Alexander I. Bobenko, Yuri B. Suris. 2007
172 citations recorded by the source corpus.
We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on ℤ2. The fields are associated with the vertices and an equation of the form Q(x1, x2, x3, x4) = 0 relates four vertices of one cell. The integrability of equations is understood as 3D-consistency, which means that it is possible to impose equations of the same type on all faces of a three-dimensional cube so that the resulting system will be consistent. This allows one to extend these equations also to the multidimensional lattices ℤN. We classify integrable equations with complex fields x and polynomials Q multiaffine in all variables. Our method is based on the analysis of singular solutions.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0070eccaf68c2a6f2c51c3e4ee87f1b62c080fa1
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Soliton Solutions for ABS Lattice Equations (2009, methodology): “The property has subsequently been used by Adler, Bobenko and Suris (ABS) [3, 4] as a classifying property.”