ABUNDANT SYMMETRIES FOR THE 1-THEORY(1 DIMENSIONAL CLASSICAL LIOUVILLE FIELD)

Explicit calculation shows us that there exists a rich associated symm etry structure and abundant strong symmetry configuration for the 1 1 dimensional classical Liouville field theory. Starting from these sy mmetries and strong symmetries, various integrable hierarchies can be obtained. The Liouville I-III hierarchies, the modified Korteweg-de Vr ies (KdV) hierarchy, the Fordy-Gibbons I, and Fordy-Gibbons II hierarc hies are just special cases while the KdV hierarchy, Caudry-Dodd-Gibbo n-Sawada-Kotera hierarchy, and Kaup-Kupershmidt hierarchy can be obtai ned by using a same Miura transformation from the modified KdV, the Fo rdy-Gibbons I and Fordy-Gibbons II hierarchies, respectively. Two type s of the generalized Riccati hierarchies are also presented.