Hamiltonian forms of the two new integrable systems and two kinds of Darboux transformations
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摘要
Based on the Lie algebra gl(2), taking a kind of corresponding loop algebra gl(2)∼, a new Lax integrable hierarchy can be obtained. Then, by means of the quadratic-form identity, the corresponding bi-Hamiltonian structure was worked out. Expanding Lie algebra gl(2), and making use of the new zero curvature equation Zhang (2008) [9], we obtain an integrable hierarchy and its Hamiltonian structure. At last, two kinds of Darboux transformations of the equation are generated.
论文关键词:Matrix Lie algebra,Quadratic-form identity,Bi-Hamiltonian structure,Darboux transformation
论文评审过程:Available online 24 July 2014.
论文官网地址:https://doi.org/10.1016/j.amc.2014.07.006