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.

• Received 3 June 1987

DOI:https://doi.org/10.1103/PhysRevLett.59.2825