Trigonal Toda lattice Equation

2019/06/10 by Matsutani, Shigeki
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1906.03792

Abstract

In this article, we give the trigonal Toda lattice equation, -(1)/(2)(d³)/(d t³) q_ℓ(t) = e^q_ℓ+1(t) +e^q_ℓ+ζ3(t) +e^q_ℓ+ζ3²(t)-3e^q_ℓ(t), for a lattice point ℓ ∈ ℤ[ζ₃] as a directed 6-regular graph where ζ₃=e^2πi/3, and its elliptic solution for the curve y(y-s)=x³, (s≠ 0).

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