The Darboux transformation associated with two-parameter lattice soliton equation |
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| Authors: | Xin-Yue Li Qiu-lan Zhao |
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| Affiliation: | 1. College of Science, Shandong University of Science and Technology, Qingdao 266590, PR China;2. Shandong Key Laboratory of Robotics and Intelligent Technology, Qingdao 266590, PR China;1. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China;2. Teaching Research Administration of Guangrao County, Dongying, Shandong 257300, China;1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China;2. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, China |
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| Abstract: | A new discrete matrix spectral problem with two arbitrary constants is introduced. The corresponding two-parameter integrable lattice soliton equation is obtained through the discrete zero curvature representation, and the resulting integrable lattice equation reduce to the Toda lattice in rational form for a special choice of the parameters. A Darboux transformation (DT) for the lattice soliton equation is constructed. As an application, an explicit solution of the two-parameter lattice soliton equation is presented. |
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