Two hierarchies of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformation |
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Institution: | 1. Department of Computer Science and Technology, Taishan College, Taian 271021, China;2. College of Science, Shandong University of Science and Technology, Qingdao 266510, China;3. College of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China |
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Abstract: | By considering a new discrete isospectral eigenvalue problem, two hierarchies of integrable positive and negative lattice models are derived. It is shown that they correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. And, each equation in the resulting hierarchies is integrable in Liouville sense. Moreover, a Darboux transformation is established for the typical equations by using gauge transformations of Lax pairs, from which the exact solutions are given. |
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