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arXiv · 2301.09298

Matrix similarity transformations derived from extended $q$-analogues of the Toda equation and Lotka-Volterra system

R. Watanabe·M. Shinjo·M. Iwasaki
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Abstract

The $q$-Toda equation is derived from replacing ordinary derivatives with $q$-derivatives in the famous Toda equation. In this paper, we associate an extension of the $q$-Toda equation with matrix eigenvalue problems, and then show applications of its time-discretization to computing matrix eigenvalues. With respect to the Lotka-Volterra system, we also have the similar discussion on the case of the Toda equation.

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R. Watanabe, M. Shinjo, M. Iwasaki. 2023-01-23. Matrix similarity transformations derived from extended $q$-analogues of the Toda equation and Lotka-Volterra system. https://doi.org/10.1080/10236198.2023.2220428

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