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Rogue waves are intense and unexpected wavepackets ubiquitous in complex systems. In optics, they are promising as robust and noise-resistant beams for probing and manipulating the underlying material. Localizing large optical power is…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS…
We have studied the modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized warm plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have…
The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g \approx…
The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous…
The standard nonlinear Schr\"{o}dinger equation (NLSE) is one of the elegant equations to find the information about the modulational instability criteria of dust-ion-acoustic (DIA) waves (DIAWs) and associated DIA rogue waves (DIARWs) in a…
In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the…
Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects…
A robust approach to excitation and control of large amplitude standing magnetization waves in an easy axis ferromagnetic by starting from a ground state and passage through resonances with chirped frequency microwave or spin torque drives…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
We address light propagation properties in complex media consisting of random distributions of lenses that have specific focusing properties. We present both analytical and numerical techniques that can be used to study emergent properties…
The coupled cubic nonlinear Schr\"odinger (CNLS) equations are used to study modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting…
A nonlinear beatwave regime of plasma wave excitation is considered. Two beatwave drivers are considered: intensity-modulated laser pulse and density-modulated (microbunched) electron beam. It is shown that a long beatwave pulse can excite…
In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane…
Partially magnetized plasmas in ExB configurations - where the electric and magnetic fields are mutually perpendicular - exhibit a cross-field transport behavior, which is widely believed to be dominantly governed by complex…
To date, axisymmetric internal wave fields, which have relevance to atmospheric internal wave fields generated by storm cells and oceanic near-inertial wave fields generated by surface storms, have been experimentally realized using an…
Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the…
The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection…
A theoretical investigation has been made to understand the mechanism of the formation of both bright and dark envelope soltions associated with dust-ion-acoustic waves (DIAWs) propagating in an unmagnetized three component dusty plasma…