Determinant Formulas for the Toda and Discrete Toda Equations
Kenji Kajiwara(Doshisha Univ.), Tetsu Masuda(Doshisha Univ.),, Masatoshi Noumi(Kobe Univ.), Yasuhiro Ohta(Hiroshima Univ.), Yasuhiko, Yamada(Kobe Univ.)
TL;DR
This paper presents determinant formulas for solving the Toda and discrete Toda equations and explores their application to Painlevé equations' tau functions.
Contribution
It introduces new determinant formulas for the general solutions of Toda and discrete Toda equations, linking them to Painlevé tau functions.
Findings
Determinant formulas for Toda solutions
Application to Painlevé tau functions
Enhanced understanding of integrable systems
Abstract
Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the functions for the Painlev\'e equations is also discussed.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Algebraic structures and combinatorial models