Positive and negative integrable hierarchies, associated conservation laws and Darboux transformation |
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Authors: | Xin-Yue Li Yuan-Qing Zhang Qiu-Lan Zhao |
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Institution: | aCollege of Science, Shandong University of Science and Technology, Qingdao, 266510, PR China |
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Abstract: | Two hierarchies of integrable positive and negative lattice equations in connection with a new discrete isospectral problem are derived. It is shown that they correspond to positive and negative power expansions respectively of Lax operators with respect to the spectral parameter, and each equation in the resulting hierarchies is Liouville integrable. Moreover, infinitely many conservation laws of corresponding positive lattice equations are obtained in a direct way. Finally, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations, by means of which the exact solutions are given. |
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Keywords: | Discrete integrable system Discrete zero curvature equation Hamiltonian structure Conservation laws Darboux transformation |
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