Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers

Karjanto, N.

doi:10.3389/fphy.2021.599767

Cited by 13 publications

(4 citation statements)

References 146 publications

(176 reference statements)

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“…This Peregrine breather solution can be obtained as a limiting case for the Akhmediev-Eleonskii-Kulagin breather when the parameters ν and µ approach zero [110,111]. In a recent breakthrough for nonlinear waves, Karjanto analytically derived the Fourier spectrum of various breather solutions, including the fundamental bright soliton, providing valuable insights into their behaviors in the spectral domain [112,113].…”

Section: Applications In Surface Gravity Wavesmentioning

confidence: 98%

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Karjanto

2024

Mathematics

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The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity waves to the captivating realm of Bose–Einstein condensates. This article delves into the dual facets of the NLS equation: its capacity for modeling wave packet dynamics and its remarkable breadth of applications. We illuminate the derivation of the NLS equation through both heuristic and multiple-scale approaches, underscoring how distinct interpretations of physical variables and governing equations give rise to varied wave packet dynamics and tailored values for dispersive and nonlinear coefficients. To showcase its versatility, we present an overview of the NLS equation’s compelling applications in four research frontiers: nonlinear optics, surface gravity waves, superconductivity, and Bose–Einstein condensates. This exploration reveals the NLS equation as a powerful tool for unifying and understanding a vast spectrum of physical phenomena.

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Section: Applications In Surface Gravity Wavesmentioning

confidence: 98%

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Karjanto

2024

Mathematics

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“…Peregrine originally proposed the analytic expression of the PS in hydrodynamics [34], and the PS is also a solution of the nonlinear Schrödinger (NLS) equation. It represents the ultimate case of the Kuznetsov-Ma (KM) soliton and Akhmediev breather (AB) [35], exhibiting both spatial and temporal localization properties. However, it was not until 2010 that Kibler et al observed the PS experimentally in optical fiber for the first time [36].…”

Section: Introductionmentioning

confidence: 99%

Peregrine soliton emits dispersive waves within graded-index multimode fibers without higher-order dispersion

Shuai,

Deng,

et al. 2024

J. Opt. Soc. Am. B

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We investigate the propagation dynamics of the Peregrine soliton, a significant prototype of rogue waves, within the graded-index multimode fibers, in the absence of higher-order dispersion. The Peregrine soliton keeps the approximate evolution trend when propagating within the graded-index multimode fibers to replace the single-mode fibers when preserving the equivalent nonlinear effect. In addition, a series of dispersive waves (also called resonant radiation) can be emitted by the Peregrine soliton, perturbated by the periodic beam oscillation caused by the spatial self-imaging effect within the graded-index multimode fibers. To be more exact, the location of the multiple resonant frequencies can be predicted using the modified quasi-phase-matching conditions, which are verified by the numerically calculated results. We can also manipulate the locations of spectral sidebands and the peak power of dispersive waves by changing the self-imaging parameter of the graded-index multimode fibers. Our findings can provide a deeper comprehension of the propagation characteristic of the Peregrine soliton within the graded-index multimode fibers and provide valuable instruction for further rich nonlinear experiments.

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“…In addition to the diverse soliton solutions of the Benney-Luke equation, similar soliton and breather-type solutions arise in other integrable systems, particularly the classical nonlinear Schrödinger (NLS) equation. In particular, the connection between the Peregrine soliton and its limiting behavior in relation to Akhmediev breathers and Kuznetsov-Ma-breathers has been explored [32,33]. Additionally, recent studies have investigated the characteristic features of the Fourier spectra of these NLS solutions [34,35].…”

Section: Introductionmentioning

confidence: 99%

Lump, Breather, Ma-Breather, Kuznetsov–Ma-Breather, Periodic Cross-Kink and Multi-Waves Soliton Solutions for Benney–Luke Equation

Vivas-Cortez,

Baloch,

Abbas

et al. 2024

Symmetry

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The goal of this research is to utilize some ansatz forms of solutions to obtain novel forms of soliton solutions for the Benney–Luke equation. It is a mathematically valid approximation that describes the propagation of two-way water waves in the presence of surface tension. By using ansatz forms of solutions, with an appropriate set of parameters, the lump soliton, periodic cross-kink waves, multi-waves, breather waves, Ma-breather, Kuznetsov–Ma-breather, periodic waves and rogue waves solutions can be obtained. Breather waves are confined, periodic, nonlinear wave solutions that preserve their amplitude and shape despite alternating between compression and expansion. For some integrable nonlinear partial differential equations, a lump soliton is a confined, stable solitary wave solution. Rogue waves are unusually powerful and sharp ocean surface waves that deviate significantly from the surrounding wave pattern. They pose a threat to maritime safety. They typically show up in solitary, seemingly random circumstances. Periodic cross-kink waves are a particular type of wave pattern that has frequent bends or oscillations that cross at right angles. These waves provide insights into complicated wave dynamics and arise spontaneously in a variety of settings. In order to predict the wave dynamics, certain 2D, 3D and contour profiles are also analyzed. Since these recently discovered solutions contain certain arbitrary constants, they can be used to describe the variation in the qualitative characteristics of wave phenomena.

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Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers

Cited by 13 publications

References 146 publications

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Peregrine soliton emits dispersive waves within graded-index multimode fibers without higher-order dispersion

Lump, Breather, Ma-Breather, Kuznetsov–Ma-Breather, Periodic Cross-Kink and Multi-Waves Soliton Solutions for Benney–Luke Equation

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