Eigenvectors of the recursion operator and a symmetry structure for the coupled KdV hierarchy

Abstract

It is shown that eigenvectors of the recursion operator L with the eigenvalue i and the inverse of the recursion operator Li L i for the coupled KdV hierarchy (CKdVH) can be obtained in terms of squared eigenfunctions of the associated linear problem. The symmetry structure and corresponding infinite dimensional Lie algebras of CKdVH are also given. Using both the local and nonlocal symmetries of CKdVH, one can obtain some exact group invariant solutions and various new infinite-dimensional and finite-dimensional integrable models.