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Classification of 3-dimensional integrable scalar discrete equations

Please always quote using this URN: urn:nbn:de:0297-zib-10667
  • We classify all integrable 3-dimensional scalar discrete affine linear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. An equation $Q_3=0$ %of such form is called integrable if it may be consistently imposed on all $3$-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 ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system.

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Metadaten
Author:Sergey Tsarev, Thomas Wolf
Document Type:ZIB-Report
Tag:Crack; FORM; REDUCE; computer algebra; discrete equations; integrable systems; large polynomial systems
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] / 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C99 None of the above, but in this section
Contributing Corporation:DFG Research Unit 565 "Polyhedral Surfaces'' (TU-Berlin)
Date of first Publication:2008/03/05
Series (Serial Number):ZIB-Report (08-13)
ArXiv Id:http://arxiv.org/abs/0706.2464
ISSN:1438-0064
ZIB-Reportnumber:08-13
Published in:Appeared in: Letters in Mathematical Physics, Volume 84, Number 1 (2008), pp. 31-39
DOI:https://doi.org/10.1007/s11005-008-0230-2
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