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Starting from a new Lie algebra G 1 , the corresponding loop algebra G1∼ 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 G2∼. With the help of variational...
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