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Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy

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Abstract

It is shown that the nonautonomous discrete Toda equation and its Bäcklund transformation can be derived from the reduction of the hierarchy of the discrete KP equation and the discrete two-dimensional Toda equation. Some explicit examples of the determinant solutions of the nonautonomous discrete Toda equation including the Askey-Wilson polynomial are presented. Finally we discuss the relationship between the nonautonomous discrete Toda system and the nonautonomous discrete Lotka-Volterra equation.

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Satoshi Tsujimoto

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  1. Satoshi Tsujimoto
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Correspondence to Satoshi Tsujimoto.

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This paper is supported in part by Grant-in-Aid for Scientific Research No. 18540214 from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.

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Tsujimoto, S. Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy. J Syst Sci Complex 23, 153–176 (2010). https://doi.org/10.1007/s11424-010-9279-y

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  • DOI: https://doi.org/10.1007/s11424-010-9279-y

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