How close are integrable and nonintegrable models: A parametric case study based on the Salerno model
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2023
Authors
Mithun, ThudiyangalMaluckov, Aleksandra

Mančić, Ana

Khare, Avinash
Kevrekidis, Panayotis G.
Article (Published version)

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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 b...e a sensitive diagnostic to that effect.
Keywords:
chaos / pattern formation / breathers / coherent structures / Hamiltonian systemsSource:
Physical Review E, 2023, 107, 2, 024202-Funding / projects:
- Ministry of Education, Science and Technological Development, Republic of Serbia, Grant no. 200017 (University of Belgrade, Institute of Nuclear Sciences 'Vinča', Belgrade-Vinča) (RS-200017)
- Ministry of Education, Science and Technological Development, Republic of Serbia, Grant no. 200124 (Univeristy of Niš, Faculty of Science) (RS-200124)
- National Science Foundation [PHY-2110030]
- National Science Foundation [DMS-2204702]
Note:
- Preprint available here: https://arxiv.org/pdf/2210.00851.pdf
Institution/Community
VinčaTY - 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 . .