Publication: Classification of 3-dimensional integrable scalar discrete equations

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Title	Classification of 3-dimensional integrable scalar discrete equations
Authors/Editors*	SP Tsarev, T Wolf
Where published*	preprint, arXiv:0706.2464
How published*	None
Year*	2007
Volume	-1
Number	-1
Pages	19 pages
Publisher
Keywords	integrable systems, discrete equations, large polynomial systems, computer algebra, Reduce, Form, Crack
Link	http://lie.math.brocku.ca/twolf/papers/TsWo07-23.pdf
Abstract	We classify all integrable 3-dimensional scalar discrete quasilinear equations Q_3=0 on an elementary cubic cell of the lattice Z^3. An equation Q_3=0$ is called integrable if it may be consistently imposed on all 3-dimensional elementary faces of the lattice Z^4. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only nontrivial (non-linearizable) integrable equation from this class is the well-known dBKP-system.