Publication Date
2022
Journal or Book Title
arXiv Preprint
Abstract
n the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentally tractable non-integrable one (the discrete nonlinear Schrödinger model). The question we ask is: for "generic" initial data, how close are the integrable to the non-integrable models? Our more precise formulation of this question is: how well is the constancy of formerly conserved quantities preserved in the non-integrable case? Upon examining this, we find that even slight deviations from integrability can be sensitively felt by measuring these formerly conserved quantities in the case of the Salerno model. However, given that the knowledge of these quantities requires a deep physical and mathematical analysis of the system, we seek a more "generic" diagnostic towards a manifestation of integrability breaking. We argue, based on our Salerno model computations, that the full spectrum of Lyapunov exponents could be a sensitive diagnostic to that effect.
DOI
https://doi.org/10.48550/arXiv.2210.00851
License
UMass Amherst Open Access Policy
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Mithun, Thudiyangal; Maluckov, Aleksandra; Mančić, Ana; Khare, Avinash; and Kevrekidis, Panayotis G., "How close are Integrable and Non-integrable Models: A Parametric Case Study Based on the Salerno Model" (2022). arXiv Preprint. 1325.
https://doi.org/10.48550/arXiv.2210.00851