The binary nonlinearization of generalized Toda hierarchy by a special choice of parameters |
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| Institution: | 1. College of Science, Shandong University of Science and Technology, Qingdao 266510, PR China;2. Shandong Key Laboratory of Robotics and Intelligent Technology, Qingdao 266510, PR China;1. College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, PR China;2. College of Teacher Education, Tianjin Normal University, Tianjin 300387, PR China;1. Department of Physics, Swansea University, Swansea, SA2 8PP, UK;2. Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain |
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| Abstract: | A new discrete matrix spectral problem with two arbitrary constants is introduced. The corresponding 2-parameter hierarchy of integrable lattice equations, which can be reduced to the hierarchy of Toda lattice, is obtained by discrete zero curvature representation. Moreover, the Hamiltonian structure and a hereditary operators are deduced by applying the discrete trace identity. Finally, an integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonlinearization for the resulting hierarchy by a special choice of parameters. |
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