Classification of Three-Dimensional Integrable Scalar Discrete Equations
نویسندگان
چکیده
We classify all integrable three-dimensional scalar discrete affine linear equations Q3= 0 on an elementary cubic cell of the lattice Z3. An equation Q3= 0 is called integrable if it may be consistently imposed on all three-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 non-trivial (nonlinearizable) integrable equation from this class is the well-known dBKP-system. Mathematics Subject Classification (2000). 37K10, 52C99.
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