Boundary conditions for two-dimensional integrable chains
Physics Letters, Section A : General, Atomic and Solid State Physics
Elsevier BV * North-Holland
68 - 72
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The symmetry method of studying boundary value problems is generalized to the multi-dimensional case. In passing from 1 + 1 dimensions to 2 + 1 dimensions the main obstacle is the existence of nonlocal variables. To overcome this obstacle we have derived additional constraints that link the nonlocal variables of different levels. As an illustration, the application of the method to the two-dimensional Toda lattice is considered. © 1997 Elsevier Science B.V.