Darboux Transformations for the (A)over-cap2n(2)-KdV Hierarchy

The (A) over cap ((2))(2n) -hierarchy can be constructed from a splitting of the Kac-Moody algebra of type (A) over cap ((1))(2n) by an involution. By choosing certain cross section of the gauge action, we obtain the (A) over cap ((2))(2n)-KdV hierarchy. They are the equations for geometric invariants of isotropic curve flows of type A, which gives a geometric interpretation of the soliton hierarchy. In this paper, we construct Darboux and Backlund transformations for the (A) over cap ((2))(2n)-hierarchy, and use it the construct Darboux transformations for the (A) over cap ((2))(2n)-KdV hierarchy and isotropic curve flows of type A. Moreover, explicit soliton solutions for these hierarchies are given.