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We investigate the interaction between a light beam and a two-dimensional photonic lattice that is photo-induced in a photorefractive crystal using partially coherent light. We demonstrate that this interaction process is associated with a…
The study of the dynamics of a surface homeomorphism in the neighbourhood of an isolated fixed point leads us to the following results. If the fixed point index is greater than 1, a family of attractive and repulsive petals is constructed,…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
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…
In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to…
Stable ring vortex solitons, featuring a bright-shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice.…
We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the…
The standard relation between the field momentum and the force is generalized for the system with a field singularity: in addition to the regular force, there appear the singular one. This approach is applied to the description of the…
A direct link between the topological complexity of magnetic media and their dynamics is established through the construction of unambiguous conservation laws for the linear and angular momenta as moments of a topological vorticity. As a…
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is…
We consider a Froehlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this 2-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y)…
The Casimir energy for the classically stable configurations of the topological solitons in 2D quantum antiferromagnets is studied by performing the path-integral over quantum fluctuations. The magnon fluctuation around the solitons…
Many microorganisms, with phytoplankton and zooplankton as prominent examples, display phototactic behaviour, that is, the ability to perform directed motion within a light gradient. Here we experimentally demonstrate that sensing of light…
The soliton resolution conjecture for evolution PDEs of dispersive type states (vaguely) that generic initial data of finite energy give rise asymptotically to a set of receding solitons and a decaying background radiation. In this letter,…
We solve numerically exactly the many-body 1D model of bosons interacting via short-range and dipolar forces and moving in the box with periodic boundary conditions. We show that the lowest energy states with fixed total momentum can be…
Fractons are topological quasiparticles with limited mobility. While there exists a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton…
We demonstrate the importance of relativistic corrections for the study of the stability of $(2+1)$-dimensional non-topological solitons with quartic self-interaction in the low-energy limit. This result is explained by the restoration of…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…
We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling…