English

Stability of the Toda equations related to a perturbed $R_i$ type recurrence relation

Classical Analysis and ODEs 2024-06-17 v1 Exactly Solvable and Integrable Systems

Abstract

In this manuscript, a modified RIR_I type recurrence relation is considered whose recurrence coefficients are perturbed by addition or multiplication of a constant. The perturbed system of recurrence coefficients is represented by Toda lattice equations, which are derived. These equations are then represented in a matrix form. With the help of this matrix representation, a known Lax pair is recovered. Inferences about the stability of resulting perturbed system of Toda equations are drawn based on numerical experiments.

Keywords

Cite

@article{arxiv.2406.09743,
  title  = {Stability of the Toda equations related to a perturbed $R_i$ type recurrence relation},
  author = {Vinay Shukla and A. Swaminathan},
  journal= {arXiv preprint arXiv:2406.09743},
  year   = {2024}
}

Comments

15 pages, 19 figures