Abstract: Starting from a subalgebra of loop algebra 1 we construct a linear isospectral problem.A type of Liouville integrable system and its bi-Hamiltonian structure are presented by the use of Tu-model again.The reductions to the integrable system give rise to the well-known Schrdinger equation and mKdV equation.Therefore,the system is called S-mKdV hierarchy.In terms of the subalgebra of A constructed,we also construct a new subalgebra G of loop algebra A with five dimensions,from which a linear isospectral form is designed.Again,using Tu-model one obtains a type of expanding integrable models of the S-mKdV hierarchy.Some expanding integrable models of hierarchies,such as BPT hierarchy,TB hierarchy etc.are also obtained by using this method.Hence,the method proposed in this paper has important applications generally.Finally as special cases,the integrable couplings of the well-known Schrdinger equation and mKdV equation are obtained.

Keywords: 
• loop algebra /
• Hamiltonian structure /
• expanding integrable model /
• Schrdinger equation /
• mKdV equation