TL;DR
The paper derives new first integrals for the Volterra chain using determinant equalities and relationships with the Toda chain, enabling analysis of periodic solutions.
Contribution
It introduces novel determinant equalities and leverages Toda chain integrals to find new first integrals for the Volterra chain.
Findings
New determinant equalities based on Wronskian formulas
First integrals for the Volterra chain derived from Toda chain
Analysis of a periodic Volterra chain with period five
Abstract
New determinant equalities were obtained based on the Wronskian formulas for a particular solution of the Volterra chain. Using the relationship between the Toda and Volterra chains, new first integrals for the Volterra chain are calculated using the first integrals for the Toda chain. Using the first integrals, a periodic Volterra chain with a period of five was considered.
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