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Algebro-Geometric Solutions for a Discrete Integrable Equation

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  • Mengshuang Tao
  • Huanhe Dong

Abstract

With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. By means of discrete zero curvature equation, we obtain a discrete integrable hierarchy. According to decomposition of the discrete systems, the new differential-difference integrable systems with two-potential functions are derived. By constructing the Abel-Jacobi coordinates to straighten the continuous and discrete flows, the Riemann theta functions are proposed. Based on the Riemann theta functions, the algebro-geometric solutions for the discrete integrable systems are obtained.

Suggested Citation

  • Mengshuang Tao & Huanhe Dong, 2017. "Algebro-Geometric Solutions for a Discrete Integrable Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-9, November.
    • Handle: RePEc:hin:jnddns:5258375
    DOI: 10.1155/2017/5258375
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    Cited by:

    1. Tongshuai Liu & Huanhe Dong, 2019. "The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    2. Lei Fu & Yaodeng Chen & Hongwei Yang, 2019. "Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids," Mathematics, MDPI, vol. 7(1), pages 1-13, January.

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