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We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing…
Equilibrium distribution of interacting ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For an arbitrarily given realization of the disorder, an exact solution of the equation is…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for…
Coherent effects manifested in light scattering from cold, optically dense and disordered atomic systems are reviewed from a primarily theoretical point of view. Development of the basic theoretical tools is then elaborated through several…
Chaos characterized by its irregularity and high sensitivity to initial conditions finds various applications in secure optical communications, random number generations, light detection and ranging systems, etc. Semiconductor lasers serve…
To probe the nonlinear effects of photon-photon interaction in the quantum electrodynamics, we study the generation of circular polarized photons by the collision of two linearly polarized laser beams. In the framework of the…
For the Nonlinear Shr\"odinger Equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear…
We consider mean-field limits for overdamped Langevin dynamics of $N$ particles with possibly singular interactions. It has been shown that a modulated free energy method can be used to prove the mean-field convergence or propagation of…
We consider the cubic defocusing nonlinear Schr\"odinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all…
Coupled nonlinear Schrodinger systems describe some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photorefractive media in optics and Bose-Einstein condensates. In this paper, we study the existence of…
We investigate a propagation of solitons for nonlinear Schr\"odinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leads to changing of number of solitons.…
Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schr\"odinger (NLS) equation. This problem is of fundamental importance as a dispersive…
In any quantum or wave system dissipation leads to decoherence. Therefore, it was surprising in first instance when experiments on strongly lossy random lasers showed unambiguously by measurements of the photon statistics and of the lasing…
Nonlinear Compton scattering (NCS) and nonlinear Breit-Wheeler (NBW) process are strongly multi-photon and highly nonlinear processes. In ultra intense lasers (normalized field amplitude $a_0 \gg 1$), radiation formation length is much…
Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schr\"odinger equations, which describe weakly…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
We report on the experimental observation of weak localization in an optically induced disordered (2+1)-dimensional photonic structure. Our flexible method of optical induction is applied with a nondiffracting random intensity distribution.…
We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear…
Matter-wave bright solitons are predicted to reflect from a purely attractive potential well although they are macroscopic objects with classical particle-like properties. The non-classical reflection occurs at small velocities and a…