Related papers: Nonlinear molecular excitations in a completely in…
The internal motions of DNA immersed in bio-fluid are investigated. The interactions between the fragments of DNA and the surrounding bio-fluid are modeled using the gauge fluid lagrangian. In the model, the bio-fluid is coupled to the…
The response of a short DNA segment to bending is studied, taking into account the anisotropy in the bending rigidities caused by the double-helical structure. It is shown that the anisotropy introduces an effective nonlinear twist-bend…
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field…
The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit…
In the present article, we introduce a model to investigate the energy spectrum of a relativistic rotor by considering the Klein-Gordon Hamiltonian. Rotational spectral lines are a signature of homonuclear and heteronuclear systems and play…
We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a…
Parts of DNA sequences known as exons and introns play very different role in coding and storage of genetic information. Here we show that their conducting properties are also very different. Taking into account long-range correlations…
This paper presents the perturbation theory for the double--sine--Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation's influence. In particular case…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending…
A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors, are…
Sine-Gordon model with variable mass (VMSG) appears in many physical systems, ranging from the current through nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or…
Soliton molecules are the manifestation of attractive and repulsive interaction between optical pulses mediated by a nonlinear medium. However, the formation and breakup of soliton molecules are difficult to observe due to the transient…
Long length-scale structural deformations of DNA play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as a viable tool to model deformations of…
We study the transport of charge due to polarons in a model of DNA which takes in account its 3D structure and the coupling of the electron wave function with the H--bond distortions and the twist motions of the base pairs. Perturbations of…
We investigate the electron (hole) transport through short double-stranded DNA wires in which the electrons are strongly coupled to the specific vibrational modes (vibrons) of the DNA. We analyze the problem starting from a tight-binding…
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…
The interaction between large internal motion of DNA surrounded by bio-fluid is investigated. The phenomenon is modelled using the relativistic Navier-Stokes lagrangian describing the bio-fluid coupled to the standard Klein-Gordon…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic…
In this article, we show how one can restore an unknown nonlinear partial differential equation of a sine-Gordon type from its linearization around an unknown stationary kink. The key idea is to regard the ground state of the linear problem…