Somos-4 equation and related equations
Classical Analysis and ODEs
2023-07-13 v1 Exactly Solvable and Integrable Systems
Abstract
The main object of study in this paper is the well-known Somos-4 recurrence. We prove a theorem that any sequence generated by this equation also satisfies Gale-Robinson one. The corresponding identity is written in terms of its companion elliptic sequence. An example of such relationship is provided by the second-order linear sequence which, as we prove using Wajda's identity, satisfies the Somos-4 recurrence with suitable coefficients. Also, we construct a class of solutions to Volterra lattice equation closely related to the second-order linear sequence.
Cite
@article{arxiv.2307.05866,
title = {Somos-4 equation and related equations},
author = {Andrei K. Svinin},
journal= {arXiv preprint arXiv:2307.05866},
year = {2023}
}
Comments
17 pages