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We study, numerically and analytically, linear and nonlinear waveguides induced by optical vortex solitons in a Kerr medium. Both fundamental and first-order guided modes are analyzed, as well as the cases of effectively defocusing and…
Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders, as exact solutions of Maxwell's equations in the presence of vectorial Kerr effect. More…
Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear…
We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S.…
The nature of traveling wave solutions to equations of hydrodynamics of a generic three-dimensional electron gas with parabolic dispersion law depends on whether the motion is subsonic or supersonic. Solitons representing localized…
This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Electrodynamics} [1]-[3] in non-relativistic terms, i.e. in terms of the electric and magnetic vector fields (${\mathbf E},{\mathbf B}$), and to…
Stationary solitary waves are studied in an array of $M$ linearly-coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons,…
We construct solitary waves for the fractional Korteweg-De Vries type equation $u_t + (\Lambda^{-s}u + u^2)_x = 0$, where $\Lambda^{-s}$ denotes the Bessel potential operator $(1 + |D|^2)^{-\frac{s}{2}}$ for $s \in (0,\infty)$. The approach…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science---and in physics in particular. Flat-top solitons are a novel type of…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry-breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states…
This article concludes the study of (2+1)-dimensional nonlinear wave equations that can be derived in a model of an ideal fluid with irrotational motion. In the considered case of identical scaling of the $x,y$ variables, obtaining a…
Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold…
We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and…
An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like…
Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (\textit{System 1} and \textit{System 2}), with the self-attractive on-site…
We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear media. The components of such mixed-gap solitons emerge from…
We study the energy-critical wave equation in three dimensions, focusing on its ground state soliton, denoted by $W$. Using the Poincar\'e symmetry inherent in the equation, boosting $W$ along any timelike geodesic yields another solution.…
We demonstrate a stable, mobile, dipolar or nondipolar three-dimensional matter-wave soliton in the vortex core of a uniform nondipolar condensate. All intra- and inter-species contact interactions can be repulsive for a strongly dipolar…