A New Integrable Hierarchy and Its Hamiltonian Structure

Starting from a isospectral problem and basing on the basis number and commutative relations of loop algerba,we propose a type of Liouville integrable system and its bi-Hamiltonian structure by the use of Tu Guizhang's model.The reductions to the integrable system give rise to the well-known Schrodinger equation,generalized MKdV equation,Heated conduction euqation and Burgers equation.This method can be used generally.