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

Shinsuke Iwao, Hidetomo Nagai

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号134002
ジャーナルJournal of Physics A: Mathematical and Theoretical
51
13
DOI
出版ステータスPublished - 2018 2月 26
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)

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