Stability of the Toda system related to a perturbed \(R_I\)-type recurrence relation

Abstract

In this manuscript, a modified \(R_I\)-type recurrence relation is considered whose recurrence coefficients are perturbed by the addition or multiplication of a constant. Using the perturbed system of recurrence coefficients, perturbed extended relativistic Toda equations are derived. These equations are then represented in a matrix form. This matrix representation helps recover a Lax pair that has already been studied in the literature. Inferences about the stability of the resulting perturbed system of the Toda equations are drawn based on numerical experiments.