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We investigate second-order nonlinear processes in a system of two coupled identical optical micro-resonators. The double resonance and phase-matching conditions are simultaneously obtained thanks to the frequency splitting induced by the…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
The method proposed in [I.R. Khairulin et al., JETP Letters 117(9), 652 (2023)] for converting the linearly polarized radiation of high-order harmonics of an optical field into the circularly polarized in an optically modulated active…
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…
We developed a new method based on functional integration to treat the dynamics of polarons in one-dimensional systems. We treat the acoustical and the optical case in an unified manner, showing their differences and similarities. The…
We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the…
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…
We study the dynamics of a pair of nonlinear split-ring resonators (a `metadimer') excited by an alternating magnetic field and coupled magnetically. Linear metadimers of this kind have been recently used as the elementary components for…
We demonstrate that a superoscillating in time signal may be obtained as a nonlinear response on a harmonic low-frequency input. Using the realization of a superoscillating function proposed by (Huang et al. 2007 J. Opt. A: Pure Appl. Opt.…
We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to…
We investigate the steady-state electronic transport through a suspended dimer molecule coupled to leads. When strongly coupled to a vibrational mode, the electron transport is enhanced at the phonon resonant frequency and higher-order…
We study evolution equations and stationary homogeneous solutions for electric and magnetic field amplitudes in a ring cavity with flat mirrors. The cavity is filled with a positive or negative refraction index material with third order…
Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix…
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity-dispersion (GVD) in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which…
Polarization- and wavelength-sensitive absorbers for homogeneous electromagnetic waves are crucial in photovoltaics, imaging and telecommunications. Here, we report on an absorber selective to the topological structure of light. An…
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…
Motivated by the recent developments in terahertz spectroscopy using pump-probe setups to study correlated electronic materials, we review the field theoretical formalism to compute finite frequency nonlinear electro-optical responses in…