论文信息 - Classification of 3-dimensional integrable scalar discrete equations

Classification of 3-dimensional integrable scalar discrete equations

We classify all integrable 3-dimensional scalar discrete quasilinear equations Q3 = 0 on an elementary cubic cell of the lattice Z 3. An equation Q3 = 0 is called integrable if it may be consistently imposed on all 3-dimensional elementary faces of the lattice Z4. 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. MSC: 37K10, 52C99

S. P. Tsarev

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