18 research outputs found
A New Expression of Soliton Solution to the Ultradiscrete Toda Equation
A new type of multi-soliton solution to the ultradiscrete Toda equation is
proposed. The solution can be transformed into another expression of solution
in a perturbation form. A direct proof of the solution is also given.Comment: 13 page
Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution
Ultradiscrete soliton equations and B\"acklund transformation for a
generalized soliton solution are presented. The equations include the
ultradiscrete KdV equation or the ultradiscrete Toda equation in a special
case. We also express the solution by the ultradiscrete permanent, which is
defined by ultradiscretizing the signature-free determinant, that is, the
permanent. Moreover, we discuss a relation between B\"acklund transformations
for discrete and ultradiscrete KdV equations.Comment: 11 page
ある行列式の超離散化について
九州大学応用力学研究所研究集会報告 No.22AO-S8 「非線形波動研究の新たな展開 : 現象とモデル化」Report of RIAM Symposium No.22AO-S8 Development in Nonlinear Wave: Phenomena and Modeling超離散化可能なある形式の行列式を紹介する.また超離散パーマネント形式で表すことで離散,超離散ソリトン方程式における既知の行列式解と超離散パーマネント解との対応を与える
Tropical Krichever construction for the non-periodic box and ball system
A solution for an initial value problem of the box and ball system is
constructed from a solution of the periodic box and ball system. The
construction is done through a specific limiting process based on the theory of
tropical geometry. This method gives a tropical analogue of the Krichever
construction, which is an algebro-geometric method to construct exact solutions
to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur
An Ultradiscrete Permanent Solution to the Ultradiscrete Two-Dimensional Toda Equation (Mathematical structures of integrable systems and their applications)
"Mathematical structures of integrable systems and their applications". September 5-7, 2018. edited by Shinsuke Iwao. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.An ultradiscrete permanent solution to the ultradiscrete two-dimensional Toda equation is proposed. The solution is obtained using an ultradiscrete analogue of the Jacobi identity with provided certain elements