Related papers: Two-state dynamics for replicating two-strand syst…
The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for…
A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of…
Renaturation of complementary single strands of DNA is one of the important processes that requires better understanding in the view of molecular biology and biological physics. Here we develop a stochastic dynamical model on the DNA…
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…
A Lax system in three variables is presented, two equations of which form the Lax pair of the stationary Davey-Stewartson II equation. With certain nonlinear constraints, the full integrability condition of this Lax system contains the…
A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyse nonlinear dynamical systems brings new strategies for…
DNA torsion dynamics is essential in the transcription process; simple models for it have been proposed by several authors, in particular Yakushevich (Y model). These are strongly related to models of DNA separation dynamics such as the one…
The dynamics of a two-state system whose energies undergo a real crossing at some instant of time is studied. At this instant, both the coupling and the detuning vanish simultaneously, which leads to an exact degeneracy of the eigenenergies…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
The relation between the Darboux transformation and the solutions of the full Kostant Toda lattice is analyzed. The discrete Korteweg de Vries equation is used to obtain such solutions and the main result of [1] is extended to the case of…
In this paper we follow the lines of recent works to investigate systems of two coupled real scalar fields defined by potentials that describe periodic interactions between the scalar fields. We work with polymeric chains containing…
We propose a model for the fluctuation dynamics of the local denaturation zones (bubbles) in double-stranded DNA. In our formulation, the DNA strand is model as a one dimensional Rouse chain confined at both the ends. The bubble is formed…
We construct the Darboux-Backlund transformation for the sigma model describing static configurations of the 2-dimensional classical continuum Heisenberg chain. The transformation is characterized by a non-trivial normalization matrix…
Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form.…
We consider the evolution of a two-mode system of bosons under the action of a Hamiltonian that generates linear SU(2) transformations. The Hamiltonian is generic in that it represents a host of entanglement mechanisms, which can thus be…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…
This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described…
In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension $n\geq 2$, stability estimates with…