2024/03/10 by Shigeki Matsutani, Matsutani, Shigeki · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic Geometry (math.AG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2403.06156
openalex publication_date 2024/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the elliptic function solutions of the nonlinear Schrödinger equation are reduced to the algebraic differential relation in terms of the Weierstrass sigma function, [-\fraki(∂)/(∂ t) +α(∂)/(∂ u)]Ψ-(1)/(2) (∂2)/(∂ u2)Ψ+(Ψ^* Ψ) Ψ= \frac12 (2β+α2-3\wp(v))Ψ, where Ψ(u;v, t):=e^αu+\frakiβt+c \frace-ζ(v)uσ(u+v)σ(u)σ(v), its dual Ψ^*(u; v,t), and certain complex numbers α, β and c. In this paper, we generalize the algebraic differential relation to those of genera two and three in terms of the hyperelliptic sigma functions.