Abstract
We classify all integrable three-dimensional scalar discrete affine linear equations Q 3 = 0 on an elementary cubic cell of the lattice \({\mathbb Z}^3\) . An equation Q 3 = 0 is called integrable if it may be consistently imposed on all three-dimensional elementary faces of the lattice \({\mathbb Z}^4\) . 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 non-trivial (non-linearizable) integrable equation from this class is the well-known dBKP-system.
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Supported by the DFG Research Unit 565 “Polyhedral Surfaces” (TU-Berlin).
SPT acknowledges partial financial support from a grant of Siberian Federal University (NM-project No 45.2007) and the RFBR grant 06-01-00814.
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Tsarev, S.P., Wolf, T. Classification of Three-Dimensional Integrable Scalar Discrete Equations. Lett Math Phys 84, 31–39 (2008). https://doi.org/10.1007/s11005-008-0230-2
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DOI: https://doi.org/10.1007/s11005-008-0230-2