Ultradiscrete Pl\"ucker Relation Specialized for Soliton Solutions
Hidetomo Nagai, Daisuke Takahashi
TL;DR
This paper introduces an ultradiscrete Pl"ucker relation tailored for soliton solutions, utilizing ultradiscrete permanents to derive solutions for ultradiscrete integrable systems like KP and Toda lattice equations.
Contribution
It develops a novel ultradiscrete Pl"ucker relation using ultradiscrete permanents, enabling explicit soliton solutions for ultradiscrete integrable equations.
Findings
Derived ultradiscrete Pl"ucker relation for soliton solutions
Constructed soliton solutions for ultradiscrete KP and Toda lattice equations
Demonstrated the effectiveness of ultradiscrete permanents in integrable systems
Abstract
We propose an ultradiscrete analogue of Pl\"ucker relation specialized for soliton solutions. It is expressed by an ultradiscrete permanent which is obtained by ultradiscretizing the permanent, that is, the signature-free determinant. Using this relation, we also show soliton solutions to the ultradiscrete KP equation and the ultradiscrete two-dimensional Toda lattice equation respectively.
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