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We consider the linear and nonlinear models of generation of the surface plasmon-polaritons on the boundary of nonmagnetic dielectric medium and nonmagnetic metal. We have shown how the three-dimensional incident wave is transformed to the…

Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the…

Three dimensional (3D) relativistic electromagnetic sub-cycle solitons were observed in 3D Particle-in-Cell simulations of an intense short laser pulse propagation in an underdense plasma. Their structure resembles that of an oscillating…

We theoretically investigate the properties of phonon-polariton inhomogeneous harmonic wave, cnoidal wave and spatial soliton propagating in boundless dielectric medium and compute the shape of nonlinear vector polariton wave. We obtain…

The main goal of the present paper is to study how polarization of photons affects their motion in a gravitational field created by a rotating massive compact object. We study propagation of the circularly polarized beams of light in a…

We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi two-dimensional reaction-diffusion equation can be reduced…

Droplet solitons are a strongly nonlinear, inherently dynamic structure in the magnetization of ferromagnets, balancing dispersion (exchange energy) with focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons have…

This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history. Some findings, such as optical solitons supported by thermal nonlinearity, and by the orientational nonlinearity…

Solitons propagating in media with higher order dispersion will shed radiation known as dispersive wave or resonant radiation, with applications in frequency broadening, deep UV sources for spectroscopy or simply fundamental studies of…

Highly spatially-squeezed polaritons, with propagation momentum significantly larger than free-space modes at the same frequency, enable varied and extreme control over light-matter interaction. Compared to other polaritons, surface magnon…

The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…

We address the properties of optical solitons that form in media with competing cubic-quintic nonlinearity and parity-time(PT)-symmetric complex-valued external potentials. The model describes the propagation of solitons in nonlinear…

Parity-time (PT) symmetry has attracted a lot of attention since the concept of pseudo-Hermitian dynamics of open quantum systems was first demonstrated two decades ago. Contrary to their Hermitian counterparts, non-conservative…

We consider the propagation of solitons in media with an imprinted transverse periodic or parabolic refractive index modulation when the modulation depth slightly fluctuates along the propagation direction. We find that, under suitable…

We consider the transformation for the point rotation frames with the angle, spatial coordinate along the axis of rotation and time as variables. The problem arises when light, propagating through 3-fold electrooptical crystal, is modulated…

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating…

We study the scattering of solitons in the nonlinear Schroedinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The…

Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity…

Using the method of separation of variables, we developed a vector nonparaxial theory for the nonlinear wave equations in strong field approximation. We found that exact localized vortex soliton solution exists for the nonlinear 3D+1 vector…

The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model…