TY - GEN A1 - Tsarev, Sergey A1 - Wolf, Thomas T1 - Classification of 3-dimensional integrable scalar discrete equations N2 - 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. T3 - ZIB-Report - 08-13 KW - integrable systems KW - discrete equations KW - large polynomial systems KW - computer algebra KW - REDUCE KW - FORM KW - Crack Y1 - 2008 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1066 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-10667 SN - 1438-0064 ER -