Related papers: 3D+1 Parametric Bright Vortex Solitons. Optical Me…
We study the properties of linear and nonlinear waveguides induced by optical vortex solitons in both self-defocusing and self-focusing nonlinear media, for the case of a saturable nonlinear response. We demonstrate that the vortex-induced…
A model derived in [14] for n near-parallel vortex filaments in a three dimensional fluid region takes into consideration the pairwise interaction between the filaments along with an approximation for motion by self-induction. The same…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. Based on the pseudo-potential…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of…
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BEC). The soliton solutions to the mean-field equations are obtained…
The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and…
We report solutions for stable compound solitons in a three-dimensional quasi-phase-matched photonic crystal with the quadratic ($\chi ^{(2)}$) nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be…
Systems of solitary-waves in the 1D Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyse the soliton-like nature of these solitary-waves, a particle analogy for the…
A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a…
We investigate existence and linear stability of coupled vortex solitons supported by cascaded four-wave mixing in a Raman active medium excited away from the resonance. We present a detailed analysis for the two- and three-component vortex…
We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity…
We study localized wave on continuous wave background analytically in a nonlinear fiber with higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. We present an exact rational W-shaped…
Vector vortex beams, featuring independent spatial modes in orthogonal polarization components, offer an increase in information density for emerging applications in both classical and quantum communication technology. Recent advances in…
Propagation of localized waves in a Fermi-Dirac distributed super dense matter at the presence of strong external magnetic fields is studied using the reductive perturbation method. Previous works indicate that localized waves break down in…
We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of…
We consider vortex solitons in large-scale arrays composed of N elliptical waveguides placed on a ring, which can be fabricated using fs-laser writing technique in transparent nonlinear dielectrics. By introducing variable twist angles…
We consider a system of nonlinear equations which can be reduced to a degenerate parabolic equation. In the case $x\in\bR^2$ we obtained necessary conditions for the existence of a weakly singular solution of heat wave type…
Using a modified version of Weinstein's argument for constrained minimization in nonlinear dispersive equations, we prove existence of solitary waves in fully nonlocally nonlinear equations, as long as the linear multiplier is of positive…
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis,…