Abstract An anti-symmetric loop algebra $\overline{A}_2$ is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov－Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra $\tilde{G}$ of the loop algebra $\tilde{A}_2$ is constructed. As its application, a new expanding integrable system with six potential functions is engendered.
Received: 22 April 2003
Revised: 03 September 2003
Accepted manuscript online:
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