Related papers: Nonlinear molecular excitations in a completely in…
We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electromagnetic waves are governed by the Landau-Lifshitz-Maxwell…
In an early work, Bernoulli shift dynamics of submanifolds was established in a neighborhood of a homoclinic tube. In this article, we will present a concrete example: sine-Gordon equation under a quasi-periodic perturbation.
We study an intermediate quantum coherent-incoherent charge transport mechanism in metal-molecule-metal junctions using B\"uttiker's probe technique. This tool allows us to include incoherent effects in a controlled manner, and thus to…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
Nonlinear dynamics of the electron-cyclotron instability driven by the electron $\mathbf{E\times B}$ current in crossed electric and magnetic field is studied. In nonlinear regime the instability proceeds by developing a large amplitude…
A study of high-order solitons in three nonlocal nonlinear Schr\"{o}dinger equations is presented, which includes the \PT-symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schr\"{o}dinger equations. General high-order…
We adopt a variational technique to study the dynamics of perturbed dissipative solitons, whose evolution is governed by a Ginzburg--Landau equation (GLE). As a specific example of such solitons, we consider a silicon-based active waveguide…
Molecular dynamic simulations are performed to investigate a long-time evolution of different type initial signals in nonlinear acoustic chains with realistic Exp-6 potential and with power ones. Finite number of long-lifetime kink-shaped…
We study the phenomenon of length scale competition, an instability of solitons and other coherent structures that takes place when their size is of the same order of some characteristic scale of the system in which they propagate. Working…
Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single…
Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially…
The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. We analyse the Riemann problem for the corresponding…
We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We…
We investigate the properties of nonlinear excitations in different types of soliton bearing systems with long-range dispersive interaction. We show that length-scale competition in such systems universally results in a multi-component…
We investigate quantum transport characteristics of a ladder model, which effectively mimics the topology of a double-stranded DNA molecule. We consider the interaction of tunneling charges with a selected internal vibrational degree of…
We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically \cite{MSSSS18DCDS, MSSSS18QIP}. It was shown that if the nonlinearity is weak, then the long time behavior of NLQWs are approximated…
It was first suggested by Englander et al to model the nonlinear dynamics of DNA relevant to the transcription process in terms of a chain of coupled pendulums. In a related paper [q-bio.BM/0604014] we argued for the advantages of an…
Biological structure and function depend on complex regulatory interactions between many genes. A wealth of gene expression data is available from high-throughput genome-wide measurement technologies, but effective gene regulatory network…
A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross-section of the position-time sine-Gordon amplitude profile. Here we…
We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger Equation (NLSE) with the following perturbations: non-parametric spatio-temporal driving of the form $f(x,t) = a \exp[i K(t) x]$, damping, and a linear term which…