Generalizations of the finite nonperiodic Toda lattice and its Darboux transformation |
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Authors: | Jian Li Chuanzhong Li |
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Affiliation: | 1.School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, China;2.College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China |
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Abstract: | In this paper, we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles. We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformation. The solutions of the generalized Toda equations are derived using the tau functions. The relationship between the generalized nonperiodic Toda lattices and Lie algebras is then be discussed and the generalized Kac-van Moerbeke hierarchy is split into generalized Toda lattices, whose integrability and Darboux transformation are studied. |
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Keywords: | Hamiltonian systems Toda lattices Darboux transformation Lie algebra Kac-van Moerbeke hierarchy |
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