Discrete hungry integrable systems -- 40 years from the Physica D paper by W. W. Symes

DOI10.1016/j.physd.2022.133422OpenAlexW4283322604MaRDI QIDQ2167987

Emiko Ishiwata, Masashi Iwasaki, Koichi Kondo, Akiko Fukuda, Masato Shinjo, Yusaku Yamamoto, Yoshimasa Nakamura

Publication date: 1 September 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2022.133422

zbMATH Keywords

eigenvalue problemsLax representationdeterminantal solutiondiscrete hungry integrable systemKostant-Toda equation

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX) Numerical analysis (65-XX)

Related Items (1)

Preface to the special issue: orthogonal polynomials and integrable systems, peakons, Toda lattices and Painlevé transcendents

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Bäcklund transformation between two integrable discrete hungry systems
• Error analysis for matrix eigenvalue algorithm based on the discrete hungry Toda equation
• Some extremal problems for strictly totally positive matrices
• A finite-step construction of totally nonnegative matrices with specified eigenvalues
• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• The solution to a generalized Toda lattice and representation theory
• Theory of nonlinear lattices
• Determinants and their applications in mathematical physics
• Integrable discrete hungry systems and their related matrix eigenvalues
• Convergence acceleration of shifted \(LR\) transformations for totally nonnegative Hessenberg matrices.
• The Kostant-Toda equation and the hungry integrable systems
• The discrete Lotka-Volterra system computes singular values
• Short note: An integrable numerical algorithm for computing eigenvalues of a specially structured matrix
• The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Calculating Laplace Transforms in Terms of the Toda Molecule
• The Toda molecule equation and the 𝜖-algorithm
• Discrete-time Volterra chain and classical orthogonal polynomials
• Conserved Quantities of “Random-Time Toda Equation”
• Conserved Quantities of a Class of Nonlinear Difference-Difference Equations
• Toda Molecule Equation and Quotient-Difference Method
• The Toda lattice. II. Existence of integrals
• Integrable Properties of a Variant of the Discrete Hungry Toda Equations and Their Relationship to Eigenpairs of Band Matrices
• Asymptotic analysis of non-autonomous discrete hungry integrable systems
• Another generalization of the box–ball system with many kinds of balls
• Periodic convergence in the discrete hungry Toda equation
• On the convergence of a solution of the discrete Lotka Volterra system
• Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization
• Integrable discretizations of the Bogoyavlensky lattices
• Product Eigenvalue Problems
• Integrals of nonlinear equations of evolution and solitary waves
• Totally positive matrices

This page was built for publication: Discrete hungry integrable systems -- 40 years from the Physica D paper by W. W. Symes