TY  - JOUR
AU  - Mithun, Thudiyangal
AU  - Maluckov, Aleksandra
AU  - Mančić, Ana
AU  - Khare, Avinash
AU  - Kevrekidis, Panayotis G.
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10641
AB  - In 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, nonintegrable one (the discrete nonlinear Schrödinger model). The question we ask is, for "generic"initial data, how close are the integrable to the nonintegrable models Our more precise formulation of this question is, How well is the constancy of formerly conserved quantities preserved in the nonintegrable 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.
T2  - Physical Review E
T1  - How close are integrable and nonintegrable models: A parametric case study based on the Salerno model
VL  - 107
IS  - 2
SP  - 024202
DO  - 10.1103/PhysRevE.107.024202
ER  - 

@article{
author = "Mithun, Thudiyangal and Maluckov, Aleksandra and Mančić, Ana and Khare, Avinash and Kevrekidis, Panayotis G.",
year = "2023",
abstract = "In 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, nonintegrable one (the discrete nonlinear Schrödinger model). The question we ask is, for "generic"initial data, how close are the integrable to the nonintegrable models Our more precise formulation of this question is, How well is the constancy of formerly conserved quantities preserved in the nonintegrable 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.",
journal = "Physical Review E",
title = "How close are integrable and nonintegrable models: A parametric case study based on the Salerno model",
volume = "107",
number = "2",
pages = "024202",
doi = "10.1103/PhysRevE.107.024202"
}

Mithun, T., Maluckov, A., Mančić, A., Khare, A.,& Kevrekidis, P. G.. (2023). How close are integrable and nonintegrable models: A parametric case study based on the Salerno model. in Physical Review E, 107(2), 024202.
https://doi.org/10.1103/PhysRevE.107.024202

Mithun T, Maluckov A, Mančić A, Khare A, Kevrekidis PG. How close are integrable and nonintegrable models: A parametric case study based on the Salerno model. in Physical Review E. 2023;107(2):024202.
doi:10.1103/PhysRevE.107.024202 .

Mithun, Thudiyangal, Maluckov, Aleksandra, Mančić, Ana, Khare, Avinash, Kevrekidis, Panayotis G., "How close are integrable and nonintegrable models: A parametric case study based on the Salerno model" in Physical Review E, 107, no. 2 (2023):024202,
https://doi.org/10.1103/PhysRevE.107.024202 . .