Related papers: Two-dimensional dissipative rogue waves due to tim…
We demonstrate numerically a method of focusing two-photon field inside one-dimensional random media. The approach is based on coherent control of backscattering achieved by adaptive spectral pulse shaping. The spectral phases of a…
In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schr\"odinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…
The issue of rogue wave lifetimes is addressed in this study, which helps to detail the general picture of this dangerous oceanic phenomenon. The direct numerical simulations of irregular wave ensembles are performed to obtain the complete…
The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e.,…
There is considerable fundamental theoretical and applicative interest in obtaining two-dimensional rogue wave similar to one-dimensional rogue wave of the nonlinear Schr\"odinger equation. Here, we first time proposes a self-mapping…
The shoaling of surface gravity waves has been acknowledged as a mechanism of rogue wave formation. This problem is generally reduced to water waves passing over a step, but non-equilibrium physics allows finite slopes to be considered.…
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…
Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…
In an oscillatory medium, a region which oscillates faster than its surroundings can act as a source of outgoing waves. Such pacemaker-generated waves can synchronize the whole medium and are present in many chemical and biological systems,…
We investigate the outbreak of anomalous quantum wavefunction amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and…
In this paper, we propose the existence and discuss the properties of rogue quantum gravitational waves. More specifically, we numerically solve the Schr\"odinger-Newton system of equations using a spectral scheme with a $4^{th}$ order…
We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold Darboux transformation formula. We consider two types of double periodic solutions as seed solutions. We identify the squared…
Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly…
We study the (1+1) focussing nonlinear Schr\"{o}dinger equation for an initial condition with compactly-supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural…
We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the…
In the numerical modelling of cascaded mid-infrared (IR) supercontinuum generation (SCG) we have studied how an ensemble of spectrally and temporally distributed solitons from the long-wavelength part of an SC evolves and interacts when…
The nonlinear propagation of optical pulses in dielectric waveguides and resonators provides a laboratory to investigate a wide range of remarkable interactions. Many of the resulting phenomena find applications in optical systems. One…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…