Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems

Complex instabilities are the major reason for drastic changes and extreme events in dynamical systems. Several modes of instability growing simultaneously with nonlinear interaction between them may lead to unforeseeable outcomes leading to catastrophic consequences. The most common examples of the...

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Main Authors: Chowdury, Amdad, Akhmediev, Nail, Chang, Wonkeun
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/157573
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1575732022-05-12T07:04:04Z Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems Chowdury, Amdad Akhmediev, Nail Chang, Wonkeun School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Nonlinear Schrödinger Equation Akhmediev Breather Complex instabilities are the major reason for drastic changes and extreme events in dynamical systems. Several modes of instability growing simultaneously with nonlinear interaction between them may lead to unforeseeable outcomes leading to catastrophic consequences. The most common examples of these instabilities are the modulation instability (MI). Studies show that an infinite number of instability modes remain active in a dynamical system. Although a one-mode MI can be analysed in the frame of a precise mathematical model, namely the Akhmediev breather, the dynamics of several concurrent MI modes referred to as the higher-order MI is very difficult to handle. We developed a unique geometrical approach that provides an entirely new and intuitive way to deal with higher-order MI. We apply this approach in description of higher-order modulation instability, multi-breather solutions, their degenerate versions and higher-order rogue waves of the nonlinear Schrödinger equation. For a system with infinitely many interacting instability modes, the band of the instability in this description is a hypercube, a multi-dimensional space of modulation frequencies. A large variety of special multi-breather and multi-rogue wave solutions of the nonlinear Schrödinger equation in this description corresponds to special points and lines within this hypercube. Funding was provided by Australian Research Council (Grant No. DP150102057). 2022-05-11T02:45:08Z 2022-05-11T02:45:08Z 2020 Journal Article Chowdury, A., Akhmediev, N. & Chang, W. (2020). Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems. Nonlinear Dynamics, 99(3), 2265-2275. https://dx.doi.org/10.1007/s11071-019-05420-9 0924-090X https://hdl.handle.net/10356/157573 10.1007/s11071-019-05420-9 2-s2.0-85076560078 3 99 2265 2275 en Nonlinear Dynamics © 2019 Springer Nature B.V. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Nonlinear Schrödinger Equation
Akhmediev Breather
spellingShingle Engineering::Electrical and electronic engineering
Nonlinear Schrödinger Equation
Akhmediev Breather
Chowdury, Amdad
Akhmediev, Nail
Chang, Wonkeun
Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
description Complex instabilities are the major reason for drastic changes and extreme events in dynamical systems. Several modes of instability growing simultaneously with nonlinear interaction between them may lead to unforeseeable outcomes leading to catastrophic consequences. The most common examples of these instabilities are the modulation instability (MI). Studies show that an infinite number of instability modes remain active in a dynamical system. Although a one-mode MI can be analysed in the frame of a precise mathematical model, namely the Akhmediev breather, the dynamics of several concurrent MI modes referred to as the higher-order MI is very difficult to handle. We developed a unique geometrical approach that provides an entirely new and intuitive way to deal with higher-order MI. We apply this approach in description of higher-order modulation instability, multi-breather solutions, their degenerate versions and higher-order rogue waves of the nonlinear Schrödinger equation. For a system with infinitely many interacting instability modes, the band of the instability in this description is a hypercube, a multi-dimensional space of modulation frequencies. A large variety of special multi-breather and multi-rogue wave solutions of the nonlinear Schrödinger equation in this description corresponds to special points and lines within this hypercube.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Chowdury, Amdad
Akhmediev, Nail
Chang, Wonkeun
format Article
author Chowdury, Amdad
Akhmediev, Nail
Chang, Wonkeun
author_sort Chowdury, Amdad
title Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
title_short Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
title_full Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
title_fullStr Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
title_full_unstemmed Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
title_sort concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems
publishDate 2022
url https://hdl.handle.net/10356/157573
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