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A generalized SHGI integrable hierarchy and its expanding integrable model
Authors:Zhang Yu-Feng
Affiliation:Institute of Mathematics, Information School, Shandong University of Sciences and Technology, Taian 271019, China
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.
Keywords:integrable system   Hamiltonian structure   loop algebra
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