Box-ball system and the nonautonomous discrete Toda lattice (Mathematical structures of integrable systems, its deepening and expansion)

MAEDA, Kazuki

Bibliographic Information

Other Title

箱玉系と非自励離散戸田格子 (可積分系数理の深化と展開)

Abstract

We discuss the theory of finite orthogonal polynomials based on elementary linear algebra and its connection to the nonautonomous discrete Toda lattice with nonperiodic finite lattice boundary condition. By using the spectral transformation technique for finite orthogonal polynomials, one can give a solution to the initial value problem of the nonautonomous discrete Toda lattice. However, this construction of the solution cannot be ultradiscretized because of so-called “negative problem". In this paper, we focus on the rigged configuration technique to solve the initial value problem of the box-ball system and consider a connection between the rigged configuration and orthogonal polynomials.

Mathematical structures of integrable systems, its deepening and expansion. September 9-11, 2019. edited by Takao Suzuki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Journal

RIMS Kokyuroku Bessatsu

RIMS Kokyuroku Bessatsu B87 79-98, 2021-08

Research Institute for Mathematical Sciences, Kyoto University

Keywords

Details 詳細情報について

CRID: 1050571470241993856

NII Article ID: 120007167309

NII Book ID: AA12196120

HANDLE: 2433/265829

ISSN: 18816193

Text Lang: ja

Article Type: departmental bulletin paper

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