Linear instability of the Peregrine breather: Numerical and analytical investigations [PDF]
Applied Numerical Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Calini, A., Schober, C. M., Strawn, M.
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Advantages and limitations of the nonlinear Schrödinger equation in describing the evolution of nonlinear water-wave groups; pp. 356–360 [PDF]
Proceedings of the Estonian Academy of Sciences, 2015 The nonlinear Schrödinger (NLS) equation is a popular and relatively simple model used extensively to describe the evolution of nonlinear water-wave groups.
Lev Shemer
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Dispersion managed generation of Peregrine solitons and Kuznetsov-Ma breather in an optical fiber [PDF]
Physics Letters A, 2021 Optical rogue waves and its variants have been studied quite extensively in the context of optical fiber in recent years. It has been realized that dispersion management in optical fiber is experimentally much more feasible compared to its nonlinear counterpart.
Dipti Kanika Mahato +3 more
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Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves
, 2012 This article is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and its deformations.
Gaillard, Pierre
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The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study [PDF]
Frontiers in Physics, 2021 Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known
Amin Chabchoub +12 more
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Higher order Peregrine breathers and multi-rogue waves solutions of the NLS equation
, 2012 This work is a continuation of a recent paper in which we have constructed a multi-parametric family of solutions of the focusing NLS equation given in terms of wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we get a family of ...
Gaillard, Pierre
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Tenth Peregrine breather solution to the NLS equation [PDF]
Annals of Physics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Differential Relations for the Solutions to the NLS Equation and Their Different Representations
Communications in Advanced Mathematical Sciences, 2019 Solutions to the focusing nonlinear Schr\"odinger equation (NLS) of order $N$ depending on $2N-2$ real parameters in terms of wronskians and Fredholm determinants are given.
Pierre Gaillard
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Chaotic transients in the switching of roto-breathers [PDF]
, 2001 By integrating a set of model equations for Josephson ladder subjected to a uniform transverse bias current we have found almost all of the kinds of breathers described in recent experiments, and closely reproduced their voltage-current characteristics ...
Richard Giles (1251693) +1 more
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Numerical study of the stability of the Peregrine breather
, 2015 The Peregrine breather is widely discussed as a model for rogue waves in deep water. We present here a detailed numerical study of perturbations of the Peregrine breather as a solution to the nonlinear Schrödinger (NLS) equations. We first address the modulational instability of the constant modulus solution to NLS.
Klein, C., Haragus, M.
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