Abstract: In this article, we explore the periodic Toda-type chain. The aim of this work is to obtain representations for the solutions of the periodic Toda-type chain with self-consistent source within the framework of the inverse spectral method for the discrete Hill equation. An efficient method for integrating the periodic Toda-type chain with self-consistent source is presented. The results can be used in modeling special types of electric transmission lines.

Keywords: Toda chain, discrete Hill Equation, self-consistent source, inverse spectral problem, trace formulas, soliton equations.