The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons
The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons
复制标题
重新审视离散 Toda 方程：对偶 β-Grothendieck 多项式、超离散化和静态孤子
DOI：
10.1088/1751-8121/aaae30
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S.Iwao and H.Nagai
中科院分区：
文献类型：
--
作者：
Takeshi Ikeda;Shinsuke Iwao and Toshiaki Maeno;S.Iwao and H.Nagai
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.
