On the proximity of Ablowitz-Ladik and discrete Nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909428171669504 |
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| author | Lytle, Madison L. Charalampidis, Efstathios G. Mantzavinos, Dionyssios Cuevas-Maraver, Jesus Kevrekidis, Panayotis G. Karachalios, Nikos I. |
| author_facet | Lytle, Madison L. Charalampidis, Efstathios G. Mantzavinos, Dionyssios Cuevas-Maraver, Jesus Kevrekidis, Panayotis G. Karachalios, Nikos I. |
| contents | In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuzentsov-Ma (KM) breathers, in physically relevant lattice nonlinear dynamical systems. Starting from the completely integrable Ablowitz-Ladik (AL) model, we demonstrate that the evolution of KM initial data is proximal to that of the non-integrable discrete Nonlinear Schrödinger (DNLS) equation for certain parameter values of the background amplitude and breather frequency. This finding prompts us to investigate the distance (in certain norms) between the evolved solutions of both models, for which we rigorously derive and numerically confirm an upper bound. Finally, our studies are complemented by a two-parameter (background amplitude and frequency) bifurcation analysis of numerically exact, KM-type breather solutions to the DNLS equation. Alongside the stability analysis of these waveforms reported herein, this work additionally showcases potential parameter regimes where such waveforms with a flat background may emerge in the DNLS setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the proximity of Ablowitz-Ladik and discrete Nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions Lytle, Madison L. Charalampidis, Efstathios G. Mantzavinos, Dionyssios Cuevas-Maraver, Jesus Kevrekidis, Panayotis G. Karachalios, Nikos I. Pattern Formation and Solitons In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuzentsov-Ma (KM) breathers, in physically relevant lattice nonlinear dynamical systems. Starting from the completely integrable Ablowitz-Ladik (AL) model, we demonstrate that the evolution of KM initial data is proximal to that of the non-integrable discrete Nonlinear Schrödinger (DNLS) equation for certain parameter values of the background amplitude and breather frequency. This finding prompts us to investigate the distance (in certain norms) between the evolved solutions of both models, for which we rigorously derive and numerically confirm an upper bound. Finally, our studies are complemented by a two-parameter (background amplitude and frequency) bifurcation analysis of numerically exact, KM-type breather solutions to the DNLS equation. Alongside the stability analysis of these waveforms reported herein, this work additionally showcases potential parameter regimes where such waveforms with a flat background may emerge in the DNLS setting. |
| title | On the proximity of Ablowitz-Ladik and discrete Nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2412.10551 |