Reductions to Korteweg-de Vries Soliton Hierarchy |
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Authors: | CHEN Jin-Bing TAN Rui-Mei GENG Xian-Guo |
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Institution: | 1. Department of Mathematics, Southeast University, Nanjing 210096, China
;2. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
;3. Department of Information and Computational Science,
Zhengzhou University of Light Industry, Zhengzhou 450002, China |
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Abstract: | Based on the nonlinearization of Lax pairs, the Korteweg-de Vries (KdV)
soliton hierarchy is decomposed into a family of finite-dimensional
Hamiltonian systems, whose Liouville
integrability is proved by means of the elliptic coordinates. By applying the
Abel-Jacobi coordinates on a Riemann surface of hyperelliptic
curve, the resulting Hamiltonian flows as well as the KdV soliton
hierarchy are ultimately reduced into linear superpositions, expressed
by the Abel-Jacobi variables. |
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Keywords: | KdV soliton hierarchy Hamiltonian systems Riemann surface Abel-Jacobi coordinates |
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