Extensions of discrete Toda lattices and their application to Box-Ball Systems II
APA
(2024). Extensions of discrete Toda lattices and their application to Box-Ball Systems II. SciVideos. https://youtube.com/live/AhMzWREH17U
MLA
Extensions of discrete Toda lattices and their application to Box-Ball Systems II. SciVideos, Oct. 23, 2024, https://youtube.com/live/AhMzWREH17U
BibTex
@misc{ scivideos_ICTS:30024,
doi = {},
url = {https://youtube.com/live/AhMzWREH17U},
author = {},
keywords = {},
language = {en},
title = {Extensions of discrete Toda lattices and their application to Box-Ball Systems II},
publisher = {},
year = {2024},
month = {oct},
note = {ICTS:30024 see, \url{https://scivideos.org/icts-tifr/30024}}
}
Abstract
It is well known that the box-ball system discovered by Takahashi and Satsuma can be obtained by the ultra-discrete analogue of the discrete integrable system, including both the ultra-discrete analogue of the KdV lattice and the ultra-discrete analogue of the Toda lattice. This mini-course will demonstrate that it is possible to derive extended models of the box-ball systems related to the relativistic Toda lattice and the fundamental Toda orbits, which are obtained from the theory of orthogonal polynomials and their extensions. We will first introduce an elementary procedure for deriving box-ball systems from discrete KP equations. Then, we will discuss the relationship between discrete Toda lattices and their extensions based on orthogonal polynomial theory, and outline the exact solutions and ultra-discretization procedures for these systems. Additionally, we will introduce the box-ball system on R, which is obtained by clarifying its relationship with the Pitman transformation in ...