DRESSING OPERATOR APPROACH TO MOYAL ALGEBRAIC DEFORMATION OF SELFDUAL GRAVITY

[摘要] Recently Strachan introduced a Moyal algebraic deformation of selfdual gravity, replacing a Poisson bracket of the Plebanski equation by a Moyal bracket. The dressing operator method in soliton theory can be extended to this Moyal algebraic deformation of selfdual gravity. Dressing operators are defined as Laurent series with coefficients in the Moyal (or star product) algebra, and turn out to satisfy a factorization relation similar to the case of the KP and Toda hierarchies. It is a loop algebra of the Moval algebra (i.e., of a W(infinity) algebra) and an associated loop group that characterize this factorization relation. The nonlinear problem is linearized on this loop group and turns out to be integrable.

[发布日期] 1994-08-01

[关键词] DRESSING OPERATOR;MOYAL ALGEBRA;SELF-DUAL GRAVITY