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 . .

TY  - JOUR
AU  - Mithun, Thudiyangal
AU  - Maluckov, Aleksandra
AU  - Manda, Bertin Many
AU  - Skokos, Charalampos
AU  - Bishop, Alan
AU  - Saxena, Avadh
AU  - Khare, Avinash
AU  - Kevrekidis, Panayotis G
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9658
AB  - The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes. © 2021 American Physical Society.
T2  - Physical Review E
T1  - Thermalization in the one-dimensional Salerno model lattice
VL  - 103
IS  - 3
SP  - 032211
DO  - 10.1103/PhysRevE.103.032211
ER  - 

@article{
author = "Mithun, Thudiyangal and Maluckov, Aleksandra and Manda, Bertin Many and Skokos, Charalampos and Bishop, Alan and Saxena, Avadh and Khare, Avinash and Kevrekidis, Panayotis G",
year = "2021",
abstract = "The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes. © 2021 American Physical Society.",
journal = "Physical Review E",
title = "Thermalization in the one-dimensional Salerno model lattice",
volume = "103",
number = "3",
pages = "032211",
doi = "10.1103/PhysRevE.103.032211"
}

Mithun, T., Maluckov, A., Manda, B. M., Skokos, C., Bishop, A., Saxena, A., Khare, A.,& Kevrekidis, P. G.. (2021). Thermalization in the one-dimensional Salerno model lattice. in Physical Review E, 103(3), 032211.
https://doi.org/10.1103/PhysRevE.103.032211

Mithun T, Maluckov A, Manda BM, Skokos C, Bishop A, Saxena A, Khare A, Kevrekidis PG. Thermalization in the one-dimensional Salerno model lattice. in Physical Review E. 2021;103(3):032211.
doi:10.1103/PhysRevE.103.032211 .

Mithun, Thudiyangal, Maluckov, Aleksandra, Manda, Bertin Many, Skokos, Charalampos, Bishop, Alan, Saxena, Avadh, Khare, Avinash, Kevrekidis, Panayotis G, "Thermalization in the one-dimensional Salerno model lattice" in Physical Review E, 103, no. 3 (2021):032211,
https://doi.org/10.1103/PhysRevE.103.032211 . .

TY  - JOUR
AU  - Mithun, Thudiyangal
AU  - Maluckov, Aleksandra
AU  - Manda, Bertin Many
AU  - Skokos, Charalampos
AU  - Bishop, Alan
AU  - Saxena, Avadh
AU  - Khare, Avinash
AU  - Kevrekidis, Panayotis G
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9660
AB  - The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.
T2  - Physical Review E
T1  - Thermalization in the one-dimensional Salerno model lattice
VL  - 103
IS  - 3
SP  - 032211
DO  - 10.1103/PhysRevE.103.032211
ER  - 

@article{
author = "Mithun, Thudiyangal and Maluckov, Aleksandra and Manda, Bertin Many and Skokos, Charalampos and Bishop, Alan and Saxena, Avadh and Khare, Avinash and Kevrekidis, Panayotis G",
year = "2021",
abstract = "The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.",
journal = "Physical Review E",
title = "Thermalization in the one-dimensional Salerno model lattice",
volume = "103",
number = "3",
pages = "032211",
doi = "10.1103/PhysRevE.103.032211"
}

Mithun, T., Maluckov, A., Manda, B. M., Skokos, C., Bishop, A., Saxena, A., Khare, A.,& Kevrekidis, P. G.. (2021). Thermalization in the one-dimensional Salerno model lattice. in Physical Review E, 103(3), 032211.
https://doi.org/10.1103/PhysRevE.103.032211

Mithun T, Maluckov A, Manda BM, Skokos C, Bishop A, Saxena A, Khare A, Kevrekidis PG. Thermalization in the one-dimensional Salerno model lattice. in Physical Review E. 2021;103(3):032211.
doi:10.1103/PhysRevE.103.032211 .

Mithun, Thudiyangal, Maluckov, Aleksandra, Manda, Bertin Many, Skokos, Charalampos, Bishop, Alan, Saxena, Avadh, Khare, Avinash, Kevrekidis, Panayotis G, "Thermalization in the one-dimensional Salerno model lattice" in Physical Review E, 103, no. 3 (2021):032211,
https://doi.org/10.1103/PhysRevE.103.032211 . .

TY  - JOUR
AU  - Dmitriev, Sergey V.
AU  - Khare, Avinash
AU  - Kevrekidis, Panayotis G.
AU  - Saxena, Avadh
AU  - Hadžievski, Ljupčo
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3466
AB  - We consider a generalized discrete phi(4) model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific value of the propagation velocity. We demonstrate that in this class of models, given a specific velocity, the problem of finding the exact moving solution is integrable. Namely, this problem originally expressed as a three-point map can be reduced to a two-point map, from which the exact moving solutions can be derived iteratively. It was also found that these high-speed kinks can be stable and robust against perturbations introduced in the initial conditions.
T2  - Physical Review E
T1  - High-speed kinks in a generalized discrete phi(4) model
VL  - 77
IS  - 5
DO  - 10.1103/PhysRevE.77.056603
ER  - 

@article{
author = "Dmitriev, Sergey V. and Khare, Avinash and Kevrekidis, Panayotis G. and Saxena, Avadh and Hadžievski, Ljupčo",
year = "2008",
abstract = "We consider a generalized discrete phi(4) model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific value of the propagation velocity. We demonstrate that in this class of models, given a specific velocity, the problem of finding the exact moving solution is integrable. Namely, this problem originally expressed as a three-point map can be reduced to a two-point map, from which the exact moving solutions can be derived iteratively. It was also found that these high-speed kinks can be stable and robust against perturbations introduced in the initial conditions.",
journal = "Physical Review E",
title = "High-speed kinks in a generalized discrete phi(4) model",
volume = "77",
number = "5",
doi = "10.1103/PhysRevE.77.056603"
}

Dmitriev, S. V., Khare, A., Kevrekidis, P. G., Saxena, A.,& Hadžievski, L.. (2008). High-speed kinks in a generalized discrete phi(4) model. in Physical Review E, 77(5).
https://doi.org/10.1103/PhysRevE.77.056603

Dmitriev SV, Khare A, Kevrekidis PG, Saxena A, Hadžievski L. High-speed kinks in a generalized discrete phi(4) model. in Physical Review E. 2008;77(5).
doi:10.1103/PhysRevE.77.056603 .

Dmitriev, Sergey V., Khare, Avinash, Kevrekidis, Panayotis G., Saxena, Avadh, Hadžievski, Ljupčo, "High-speed kinks in a generalized discrete phi(4) model" in Physical Review E, 77, no. 5 (2008),
https://doi.org/10.1103/PhysRevE.77.056603 . .