On a Variable Transformation Between Two Integrable Systems: The Discrete Hungry Toda Equation and the Discrete Hungry Lotka-Volterra System

2010 ◽  
Author(s):  
Yusaku Yamamoto ◽  
Akiko Fukuda ◽  
Masashi Iwasaki ◽  
Emiko Ishiwata ◽  
Yoshimasa Nakamura ◽  
...  
Keyword(s):  
Integrable Systems ◽  
Toda Equation ◽  
Volterra System ◽  
Variable Transformation ◽  
Discrete Hungry Toda Equation

The Kostant-Toda equation and the hungry integrable systems

2020 ◽  
Vol 483 (2) ◽  
pp. 123627
Author(s):  
Masato Shinjo ◽  
Masashi Iwasaki ◽  
Koichi Kondo
Keyword(s):  
Integrable Systems ◽  
Toda Equation

Periodic convergence in the discrete hungry Toda equation

2018 ◽  
Vol 51 (34) ◽  
pp. 344001
Author(s):  
You Takahashi ◽  
Masashi Iwasaki ◽  
Akiko Fukuda ◽  
Emiko Ishiwata ◽  
Yoshimasa Nakamura
Keyword(s):  
Toda Equation ◽  
Discrete Hungry Toda Equation

On a shifted LR transformation derived from the discrete hungry Toda equation

2012 ◽  
Vol 170 (1) ◽  
pp. 11-26 ◽  
Author(s):  
Akiko Fukuda ◽  
Yusaku Yamamoto ◽  
Masashi Iwasaki ◽  
Emiko Ishiwata ◽  
Yoshimasa Nakamura
Keyword(s):  
Toda Equation ◽  
Discrete Hungry Toda Equation

Integrable Properties of a Variant of the Discrete Hungry Toda Equations and Their Relationship to Eigenpairs of Band Matrices

2017 ◽  
Vol 7 (4) ◽  
pp. 785-798 ◽  
Author(s):  
Yusuke Nishiyama ◽  
Masato Shinjo ◽  
Koichi Kondo ◽  
Masashi Iwasaki
Keyword(s):  
General Solution ◽  
Integrable Systems ◽  
Toda Equation ◽  
Matrix Representations ◽  
Band Matrices ◽  
Discrete Integrable Systems ◽  
Time Discretisation ◽  
Generalized Time ◽  
Computation Of Eigenvalues ◽  
Toda Equations

AbstractThe Toda equation and its variants are studied in the filed of integrable systems. One particularly generalized time discretisation of the Toda equation is known as the discrete hungry Toda (dhToda) equation, which has two main variants referred to as the dhTodaI equation and dhTodaII equation. The dhToda equations have both been shown to be applicable to the computation of eigenvalues of totally nonnegative (TN) matrices, which are matrices without negative minors. The dhTodaI equation has been investigated with respect to the properties of integrable systems, but the dhTodaII equation has not. Explicit solutions using determinants and matrix representations called Lax pairs are often considered as symbolic properties of discrete integrable systems. In this paper, we clarify the determinant solution and Lax pair of the dhTodaII equation by focusing on an infinite sequence. We show that the resulting determinant solution firmly covers the general solution to the dhTodaII equation, and provide an asymptotic analysis of the general solution as discrete-time variable goes to infinity.

Error analysis for matrix eigenvalue algorithm based on the discrete hungry Toda equation

2012 ◽  
Vol 61 (2) ◽  
pp. 243-260 ◽  
Author(s):  
Akiko Fukuda ◽  
Yusaku Yamamoto ◽  
Masashi Iwasaki ◽  
Emiko Ishiwata ◽  
Yoshimasa Nakamura
Keyword(s):  
Error Analysis ◽  
Toda Equation ◽  
Matrix Eigenvalue ◽  
Discrete Hungry Toda Equation

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

Sign in / Sign up

Export Citation Format

Share Document