The discrete Toda equation revisited: Dual β-Grothendieck polynomials, ultradiscretization, and static solitons

Shinsuke Iwao, Hidetomo Nagai

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

This paper presents a study of the discrete Toda equation that was introduced in 1977. In this paper, it is proved that the determinantal solution of the discrete Toda equation, obtained via the Lax formalism, is naturally related to the dual Grothendieck polynomials, a K-theoretic generalization of the Schur polynomials. A tropical permanent solution to the ultradiscrete Toda equation is also derived. The proposed method gives a tropical algebraic representation of the static solitons. Lastly, a new cellular automaton realization of the ultradiscrete Toda equation is proposed.

Original languageEnglish
Article number134002
JournalJournal of Physics A: Mathematical and Theoretical
Volume51
Issue number13
DOIs
Publication statusPublished - 2018 Feb 26
Externally publishedYes

Keywords

  • cellular automaton
  • determinant solutions
  • discrete Toda equation
  • dual Grothendieck Polynomial
  • ultradiscrete systems

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

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