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The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations

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Abstract

A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, Jiangsu, 210096, People’s Republic of China

    Jinbing Chen

  2. Department of Mathematics, University of Texas—Pan American, Edinburg, TX, 78539, USA

    Zhijun Qiao

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  1. Jinbing Chen
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  2. Zhijun Qiao
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Correspondence to Zhijun Qiao.

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Chen, J., Qiao, Z. The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations. Math Phys Anal Geom 14, 171–183 (2011). https://doi.org/10.1007/s11040-011-9092-4

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