Related papers: Soliton pinning by long-range order in aperiodic s…
The sine-Gordon model with space- and time-dependent parameters is considered. A highly accurate effective model with two degrees of freedom is constructed, allowing the description of the kink movement in this model even for extremely long…
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider…
Nonlinear space-time dynamics, defined in terms of celebrated 'solitonic' equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
In this thesis, we first review the linearized soliton perturbation theory developed in recent years, which is particularly simple in the one-kink sector. Using it, the amplitude and probability of kink-meson inelastic scattering can be…
Most periodic systems are governed by short-range interactions as long-range interactions in these systems diminish uniformly. In this letter, however, we demonstrate that this is not true for a more general class of systems, which possess…
We consider a polaron model where molecular \emph{rotations} are important. Here, the usual hopping between neighboring sites is affected directly by the electron-phonon interaction via a {\em twist-dependent} hopping amplitude. This model…
We study the real-time evolution of solitary excitations in 1-d quantum spin chains using exact diagonalization (ED) and the density-matrix renormalization group (DMRG). The underlying question of this work is the correspondence between…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either…
We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to…
Localised structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of lengthscales, the width of the pinning region is…
In this paper we consider two models of soliton dynamics (the sine Gordon and the \phi^4 equations) on a 1-dimensional lattice. We are interested in particular in the behavior of their kink-like solutions inside the Peierls- Nabarro barrier…
The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein…
Spontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting and knot complexity increase by orders of magnitude in diblock polymers with a fraction…
The paper presents results of numerical experiments simulating Bloch oscillations of solitons in a deformable molecular chain in a constant electric field. By the example of a homogeneous polynucleotide chain it is shown that the system…
We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related…
In this article, we study kink soliton configurations in interacting scalar field theories containing two fields without $SO(2)$ invariance. We study a class of such theories, the well-known Montonen-Sarker-Trullinger-Bishop model is one of…
We investigate the dynamics of solitons in generalized Klein-Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and…
We study periodic, quasi-periodic (Thue-Morse, Fibonacci, Period Doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in…