Related papers: Solitons supported by complex PT symmetric Gaussia…
This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…
There is a lack of knowledge about the topological invariants of non-linear $d$-dimensional systems with a periodic potential. We study these systems through a classification of the linearized NLS/GP equation around their soliton solutions.…
We show theoretically that dark solitons can exist in the presence of pure quartic dispersion, and also in the presence of both quadratic and quartic dispersive effects, displaying a much greater variety of possible solutions and dynamics…
We study collisions of moving nonlinear-Schr\"{o}dinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and,…
It is shown that the pair plasmas with small temperature asymmetry can support existence of localized as well as de-localized optical vortex solitons. Coexistence of such solitons is possible due to peculiar form of saturating nonlinearity…
We study localized two- and three-dimensional Langmuir solitons in the framework of model based on generalized nonlinear Schr\"odinger equation that accounts for local and nonlocal contributions to electron-electron nonlinearity. General…
The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in…
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 study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…
We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum…
We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core…
Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend to be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with the cubic self-focusing, creates…
We show the existence of stable two- and three-dimensional vortex solitons carrying multiple, spatially separated, single-charge topological dislocations nested around a vortex-ring core. Such new nonlinear states are supported by…
We establish existence and stabilty results for solitons in noncommutative scalar field theories in even space dimension $2d$. In particular, for any finite rank spectral projection $P$ of the number operator ${\mathcal N}$ of the…
We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into…
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…
Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear…
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities and numerically find…
Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…