Classification of 3-dimensional integrable scalar discrete equations

S. P. Tsarev; T. Wolf

doi:10.1007/s11005-008-0230-2

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arXiv · 0706.2464

Classification of 3-dimensional integrable scalar discrete equations

S. P. Tsarev·T. Wolf

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Abstract

We classify all integrable 3-dimensional scalar discrete quasilinear equations Q=0 on an elementary cubic cell of the 3-dimensional lattice. An equation Q=0 is called integrable if it may be consistently imposed on all 3-dimensional elementary faces of the 4-dimensional lattice. 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. (Version 2: A small correction in Table 1 (p.7) for n=2 has been made.) (Version 3: A few small corrections: one more reference added, the main statement stated more explicitly.)

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BibTeX RIS

S. P. Tsarev, T. Wolf. 2007-11-02. Classification of 3-dimensional integrable scalar discrete equations. https://doi.org/10.1007/s11005-008-0230-2

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