Finite-Band Solutions for the Hierarchy of Coupled Toda Lattices |
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Authors: | Xin Zeng Xianguo Geng |
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Institution: | 1.School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,People’s Republic of China |
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Abstract: | Based on the characteristic polynomial of Lax matrix for the hierarchy of coupled Toda lattices associated with a \(3\times3\) discrete matrix spectral problem, we introduce a trigonal curve with two infinite points, from which we establish the associated Dubrovin-type equations. The asymptotic properties of the meromorphic function and the Baker-Akhiezer function are studied near two infinite points on the trigonal curve. Finite-band solutions of the entire hierarchy of coupled Toda lattices are obtained in terms of the Riemann theta function. |
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