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Vacuum curves and classical integrable systems in \(2+1\) discrete dimensions. (English. Russian original) Zbl 0982.37075

J. Math. Sci., New York 94, No. 4, 1620-1629 (1999); translation from Zap. Nauchn. Semin. POMI 235, 273-286 (1996).
The author demonstrates that the vacuum curves can also be useful in studies of classical field theory by models. A difference equation on the (2+1)-dimensional cubic lattice is presented. For this equation the solution of the Cauchy problem is constructed by a rather simple method. The evolution of the system has hyperbolic character, i.e. has a finite propagation speed.

MSC:

37K60 Lattice dynamics; integrable lattice equations
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

References:

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