DARBOUX TRANSFORMATIONS FOR A LAX INTEGRABLE SYSTEM IN 2N DIMENSIONS

A 2n-dimensional Lax integrable system is proposed by a set of specifi c spectral problems. It contains Takasaki equations, the self-dual Yan g-Mills equations and its integrable hierarchy as examples. An explici t formulation of Darboux transformations is established for this Lax i ntegrable system. The Vandermonde and generalized Cauchy determinant f ormulas lead to a description for deriving explicit solutions and thus some rational and analytic solutions are obtained.