Related papers: Breather-like solitons extracted from the Peregrin…
We present experimental evidence of the universal emergence of the Peregrine soliton predicted in the semi-classical (zero-dispersion) limit of the focusing nonlinear Schr\"{o}dinger equation [Comm. Pure Appl. Math. {\bf 66}, 678 (2012)].…
Being considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schr\"odinger equation (NLS) has been recently observed and intensely investigated experimentally in particular…
We present a detailed study of the phase properties of rational breather waves observed in the hydrodynamic and optical domains, namely the Peregrine soliton and related second-order solution. At the point of maximum compression, our…
This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schr\"odinger (NLS) equation. These breathers belong to the families of solitons on a non-vanishing and constant background, where the…
The data recorded in optical fiber [1] and in hydrodynamic [2] experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral…
We report on experimental results where a temporal intensity profile presenting some of the main signatures of the Peregrine soliton (PS) is observed. However, the emergence of a highly peaked structure over a continuous background in a…
Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant excess of the operating current over the starting value, when the generation of electromagnetic pulses with anomalously large…
Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. As an exact breather solution of the one-dimensional…
In this article, we derive exact analytical expressions for the spatial Fourier spectrum of the soliton family on a constant background. Also known as breathers, these solitons are exact solutions of the nonlinear Schr\"odinger equation and…
Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation…
Soliton and breather solutions of the nonlinear Schr\"odinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such…
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied…
In this work, based on the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlocal nonlinear Schr\"odinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for…
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…
We address the various initial excitations of the Peregrine rogue wave and establish a robust transmission scheme of high power pulses extracted from the Peregrine rogue wave in a standard telecommunications fiber. The results show that the…
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 Schr\"odinger (NLS) equations. We…
The Peregrine soliton is often considered as a prototype of the rogue waves. After recent advances in the semi-classical limit of the 1-D focusing Nonlinear Schr\"odinger (NLS) equation this conjecture can be seen from another perspective.…
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…
We study a variable-coefficient nonlinear Schr\"odinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multi-peak…
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlinear Schrodinger system with parity-time…