Darboux Transformations for the A^2n(2)-KdV Hierarchy.

The A ^ 2 n (2) -hierarchy can be constructed from a splitting of the Kac–Moody algebra of type A ^ 2 n (1) by an involution. By choosing certain cross section of the gauge action, we obtain the A ^ 2 n (2) -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 Bäcklund transformations for the A ^ 2 n (2) -hierarchy, and use it the construct Darboux transformations for the A ^ 2 n (2) -KdV hierarchy and isotropic curve flows of type A. Moreover, explicit soliton solutions for these hierarchies are given. [ABSTRACT FROM AUTHOR]