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Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows

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Abstract

From the isospectral problem which we design, a \((1+1)\)-dimensional discrete integrable hierarchy is generated with the help of a loop algebra. After that we get a differential–difference integrable system with two potential functions. Finally, the algebro-geometric solution of the integrable system is obtained by straightening out the continuous and discrete flow and utilizing the Riemann–Jacobi inversion theorem.

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Acknowledgements

This work is supported by the SDUST Research Fund (2014TDJH102) and completed with the support by National Natural Science Foundation of China (No. 61402265).

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Authors and Affiliations

  1. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yu Liu, Huanhe Dong & Yong Zhang

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  1. Yu Liu
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  2. Huanhe Dong
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Correspondence to Huanhe Dong.

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Liu, Y., Dong, H. & Zhang, Y. Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows. Anal.Math.Phys. 9, 465–481 (2019). https://doi.org/10.1007/s13324-018-0209-9

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