New extended Lie algebra and the generalized integrable Liouville hierarchy

作者：Zhao Weidong; Dong Huanhe; Wang Hui^*

来源：Applied Mathematics and Computation, 2011, 218(2): 643-650.

DOI：10.1016/j.amc.2011.06.001

• Lie algebra
• Loop algebra
• Variational identity
• Hamiltonian structures
• Liouville integrable

Starting from a new Lie algebra G(1), the corresponding loop algebra (G(1)) over tilde is presented, from which a Liouville integrable hierarchy is given by using of variational identity. It follows that an expanding Lie algebra G(2) is obtained based on G(1), furthermore, a related Lax integrable hierarchy is presented by making use of its related loop algebra (G(2)) over tilde. With the help of variational identity, it is not difficult to prove that the hierarchy has Hamiltonian structure and is Liouville integrable. It is also can be seen that the second hierarchy is the expanding model of the first one.

• 出版日期2011-9-15
• 单位山东科技大学; 上海大学