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Review on the Stability of the Peregrine and Related Breathers [PDF]
Frontiers in Physics, 2020 In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev.
Miguel Alejo +2 more
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Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers [PDF]
Frontiers in Physics, 2021 This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger equation. These breathers belong to the family of solitons on a non-vanishing and constant background, where the continuous-wave envelope serves as a ...
Natanael Karjanto
exaly +7 more sources
Frontiers in Physics, 2022 A class of generalized homoclinic solutions of the nonlinear Schrödinger (NLS) equation in 1+1 dimensions is studied. These are homoclinic breathers that are shown to be derivable from the ratio of Riemann theta functions for the genus-2 solutions of ...
Alfred R Osborne
exaly +4 more sources
Akhmediev breathers and Peregrine solitary waves in a quadratic medium [PDF]
Optics Letters, 2017 We investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave, in a dispersive quadratic medium. We show the existence of quadratic Akhmediev breathers and Peregrine solitary waves, in the regime of cascading second-harmonic generation.
Fabio Baronio
exaly +5 more sources
Higher order Peregrine breathers solutions to the NLS equation
Journal of Physics: Conference Series, 2015 The solutions to the one dimensional focusing nonlinear Schrodinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N + 1) in x and t. These solutions depend on 2N – 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PN ...
Gaillard, Pierre
exaly +5 more sources
Peregrine breathers as design waves for wave-structure interaction
Ocean Engineering, 2016 This paper introduces the Peregrine breather solution of the nonlinear Schrödinger-type equation as an innovative design wave. The major benefits are the potential to generate abnormal waves of certain frequency up to physically possible wave heights, the symmetrical abnormal wave shape and the availability of an analytical solution.
Miguel Onorato +2 more
exaly +4 more sources
Editorial: Peregrine Soliton and Breathers in Wave Physics: Achievements and Perspectives [PDF]
Frontiers in Physics, 2021 Bertrand Kibler +2 more
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Multi-parametric Deformations of Peregrine Breathers Solutions to the NLS Equation
Advances in Research, 2015 Aims/ The structure of the solutions to the one dimensional focusing nonlinear Schr¨odinger equation (NLS) for the order N in terms of quasi rational functions is given here. We first give the proof that the solutions can be expressed as a ratio of two wronskians of order 2N and then two determinants by an exponential depending on t with 2N − 2 ...
Pierre Gaillard
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Numerical Simulations of Peregrine Breathers Using a Spectral Element Model
Volume 11A: Honoring Symposium for Professor Carlos Guedes Soares on Marine Technology and Ocean Engineering, 2018 Breather solutions to the nonlinear Schrödinger equation have been put forward as a possible prototype for rouge waves and have been studied both experimentally and numerically. In the present study, we perform high resolution simulations of the evolution of Peregrine breathers in finite depth using a fully nonlinear potential flow spectral element ...
Claes Eskilsson +1 more
exaly +3 more sources
Breather Structures and Peregrine Solitons in a Polarized Space Dusty Plasma [PDF]
Frontiers in Physics, 2020 In this theoretical investigation, we have examined the combined effects of nonthermally revamped polarization force on modulational instability MI of dust acoustic waves DAWs and evolution of different kinds of dust acoustic (DA) breathers in a dusty ...
Kuldeep Singh, N. S. Saini
doaj +2 more sources