Lax matrices for a 1-parameter subfamily of van Diejen--Toda chains

In this paper, we construct Lax matrices for certain relativistic open Toda chains endowed with a one-sided 1-parameter boundary interaction. Built upon the Lax representation of the dynamics, an algebraic solution algorithm is also exhibited. To our best knowledge, this particular 1-parameter subfamily of van Diejen–Toda chains has not been analyzed in earlier literature.