LIE ALGEBRAIC STRUCTURES OF (1-DIMENSIONAL LAX INTEGRABLE SYSTEMS(1))

An approach of constructing isospectral flows K-l, nonisospectral flow s sigma(k) and their implicit representations of a general Lax integra ble system is proposed. By introducing product function matrices, it i s shown that the two sets of flows and of related symmetries both cons titute infinite-dimensional Lie algebras with respect to the commutato r [.,.] given in this paper. Algebraic properties for some well-known integrable systems such as the AKNS system, the generalized Harry Dym system, and the n-wave interaction system are obtained as particular e xamples. (C) 1996 American Institute of Physics.