Related papers: Dynamics of the topological structures in inhomoge…
We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices solitons centered on cubic domains may be stabilized even in…
We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer than the mere conservation of vorticity impose an elaborate dynamical behavior…
We demonstrate the existence and stability of one-dimensional (1D) topological kink configurations immersed in higher-dimensional bosonic gases and nonlinear optical setups. Our analysis pertains, in particular, to the two- and…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy.…
We address the existence and properties of solitons in layered thermal media made of alternating focusing and defocusing layers. Such structures support robust bright solitons even if the averaged nonlinearity is defocusing. We show that…
We begin an investigation of inhomogeneous structures in holographic superfluids. As a first example, we study domain wall like defects in the 3+1 dimensional Einstein-Maxwell-Higgs theory, which was developed as a dual model for a…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
This thesis presents an extensive analysis of the behavior of topological solitons when one or more of their internal modes are activated. The first part of this manuscript is devoted to the study of the simplest topological solitons in…
Topological materials exhibit properties dictated by quantised invariants that make them robust against perturbations. This topological protection is a universal wave phenomenon that applies not only in the context of electrons in…
This Letter deals with topological solitons in an O(3) sigma model in three space dimensions (with a Skyrme term to stabilize their size). The solitons are classified topologically by their Hopf number N. The N=2 sector is studied; in…
Heterogeneous media constitute random disordered environments where transport is drastically hindered. Employing extensive molecular dynamics simulations, we investigate the spatio-temporal dynamics of tracer particles in the Lorentz model…
The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are…
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability are investigated. The different scenarios…
We report an observation of a stable soliton-like structure on the surface of a ferrofluid, generated by a local perturbation in the hysteretic regime of the Rosensweig instability. Unlike other pattern-forming systems with localized 2D…
Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and,…
The dynamics of light beams in the nonlinear optical media with periodically modulated in the longitudinal direction parity-time distribution of the complex refractive index is investigated. The possibility of dynamical stabilization of…
This article presents an overview of experimental efforts in recent years related to multidimensional solitons in Bose-Einstein condensates. We discuss the techniques used to generate and observe multidimensional nonlinear waves in…
We address the evolution of higher-order excited states, such as vortex and multi-hump solitons, in nonlocal media with synthetic, competing focusing and defocusing nonlinearities with different nonlocal transverse scales. We reveal that…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…