Related papers: Twisted toroidal vortex-solitons in inhomogeneous …
The problem of stability and spectrum of linear excitations of a soliton (kink) of the dispersive sine-Gordon and $\varphi^4$ - equations is solved exactly. It is shown that the total spectrum consists of a discrete set of frequencies of…
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…
The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…
By coating a three-dimensional topological insulator (TI) with a ferromagnetic film supporting an in-plane magnetic vortex, one breaks the time-reversal symmetry (TRS) without generating a mass gap. It rather yields electronic states bound…
Magnetic hopfions are localized magnetic solitons with non-zero 3D topological charge (Hopf index). Here I present an analytical calculation of the toroidal magnetic hopfion vector potential, emergent magnetic field, the Hopf index, and the…
We investigate a mechanism to produce superconductivity by strong purely repulsive interactions for flat dispersion $\varepsilon \sim k^4$, without using pairing instability in Fermi-liquid. The resulting superconductors break both…
Dynamics of interaction of topological solitons (vortices) in (2+1)-dimensional O(3) nonlinear sigma model in anisotropic case are investigated. By numerical simulation methods is shown that the changes of rotation frequency of isotopic…
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 self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrodinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial…
Magnetic spin topological textures recently found their electrical counterparts in polar topologies emerging from the condensation of inhomogeneous polar atomic distortions. Here, we further extend the concept to other non-polar atomic…
We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a…
We demonstrate that an array of discrete waveguides on a slab substrate, both featuring the $\chi^{2}$ nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite solitons are…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model…
We show that higher-order topological insulators can be created from usual square structure by twisting waveguides in each unit cell around the axis passing through the center of the unit cell, even without changing intracell distance…
In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…
We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are…
We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase…
We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a non-zero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions…
We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schr\"odinger-Poisson (or Newton-Schr\"odinger) equation accounting for gravitational interactions. We…