TL;DR
This paper investigates a coupled KdV-like system, revealing an integrable reduction linked to the Volterra chain, and constructs hyperelliptic solutions based on this connection.
Contribution
It identifies an integrable reduction of a non-integrable coupled KdV system related to the Volterra chain and constructs explicit hyperelliptic solutions.
Findings
Existence of an integrable reduction related to the Volterra chain
Construction of hyperelliptic solutions for the coupled KdV system
Insight into the integrability properties of the system
Abstract
This paper is devoted to the system of coupled KdV-like equations. It is shown that this apparently non-integrable system possesses an integrable reduction which is closely related to the Volterra chain. This fact is used to construct the hyperelliptic solutions of the original system.
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