An asymptotic expansion of the Casorati determinant and its application to discrete integrable systems

2013/10/09 by Masato Shinjo, Shinjo, Masato, Masashi Iwasaki +3
Chemistry · Mathematics · Medicine · Physics and Astronomy · #15A15 #34E05 #39A12 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Molecular spectroscopy and chirality #math-ph #math.DS #math.MP #msc:15A15 #msc:34E05 #msc:39A12

paper · pdf · doi:10.48550/arxiv.1310.2407

12 pages

arxiv created 2013/10/09 · openalex publication_date 2013/10/09 · arxiv updated 2013/10/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Hankel determinant appears in the representation of solutions to several integrable systems. Asymptotic expansion of the Hankel determinant thus plays a key role for investigating asymptotic analysis of such integrable system. In this paper, an asymptotic expansion formula of a certain Casorati determinant is presented as an extension of the Hankel case. It is also shown that an application of it to an asymptotic analysis of the discrete hungry Lotka-Volterra system, which is one of basic models in mathematical biology.

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