Abstract
The Davey-Stewartson I equation is a nonlinear evolution equation originally derived in the context of multidimensional, weakly nonlinear water waves. It has recently been exactly solved by the classical inverse-scattering method for localized potentials, and also possesses nonlocal soliton solutions. We have calculated Poisson-bracket relations for elements of the scattering matrix, as well as corresponding quantum commutation relations. Commutation relations are found that are a (2+1)-dimensional generalization of a Yang-Baxter algebra.
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