Related papers: Nonlinear molecular excitations in a completely in…
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…
The Kirchhoff elastic theory of thin filaments with spontaneous curvature is employed in the understanding of the onset of the kink transitions observed in short DNA rings. Dynamical analysis shows that when its actual curvature is less…
In this paper we study the phenomenon of nonlinear supratransmission in a semi-infinite discrete chain of coupled oscillators described by modified sine-Gordon equations with constant external and internal damping, and subject to harmonic…
This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We…
In the present work, we explore the possibility of excited breather states in a nonlinear Klein--Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this fundamentally nonlinear…
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena…
DNA torsion dynamics is essential in the transcription process; a simple model for it, in reasonable agreement with experimental observations, has been proposed by Yakushevich (Y) and developed by several authors; in this, the DNA subunits…
Evolution of the nonequilibrium inhomogeneities and topological defects is studied in terms of complex kink solutions of the sine-Gordon equation. The weakly damped oscillation of the sine-Gordon kink, named as the kink quasimode, is…
We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of partial differential equations describing the dynamics of…
We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a…
Conformational change of a DNA molecule is frequently observed in multiple biological processes and has been modelled using a chain of strongly coupled oscillators with a nonlinear bistable potential. While the mechanism and properties of…
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…
The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and…
An impact of kink-type solitons on infrared lattice vibrations is studied for incommensurate Frenkel-Kontorova model. It is shown that the vibration of particles involved into the kink formation is very similar to that in a gap mode around…
Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform…
We present the results of our numerical analysis of a "composite" model of DNA which generalizes a well-known elementary torsional model of Yakushevich by allowing bases to move independently from the backbone. The model shares with the…
Intracellular positive ions neutralise negative charges on the phosphates of a DNA strand conferring greater strength on the hydrogen bonds that connect complementary strands into a double helix and so confer enhanced stability. Beyond a…
It has been suggested by several authors that nonlinear excitations, in particular solitary waves, could play a fundamental functional role in the process of DNA transcription, effecting the opening of the double chain needed for RNA…
Analyses of high energy elastic pp and $\bar pp$ scattering data from CERN ISR and SPS Collider seem to provide strong evidence in favor of the gauged nonlinear sigma-model of the nucleon. This model describes the nucleon as a topological…