33 research outputs found
Modulational instability in optical fiber with stochastic parameters and noninstantaneous response
Exact localized solutions of the (2+1)-dimensional complex cubic-quintic Ginzburg-Landau equation
Wave propagation of nonlinear modes and formation of bubble in a two-component helicoidal lattice
Through the multiple
scale expansion, we show that the dynamics of modulated waves in a
two-component helicoidal one-dimensional model is governed by the
nonlinear Schrödinger (NLS) equation. We study the occurrence of
patterns formation in such a system. The impact of the helicoidal
coupling is also studied which reveals that high values of the
helicoidal coupling constant contribute to regulate information and
charge transport throughout the two-chain model. This is made
possible due to the superposition of optical and acoustic modes. In
addition, the model is used to investigate internal dynamics of DNA.
It is shown that the opening of the double helix of the DNA itself
is controlled by the resonance mode, where the unzipping of the
double helix has been illustrated by numerical simulations.
Furthermore, the shape of the eyelike shape previously observed in
experiments of thermal denaturation of DNA is numerically obtained
Domain wall motion in ferromagnets modelled by a quintic complex Ginzburg-Landau equation
A quintic complex Ginzburg-Landau equation is derived from a
Landau-Lifshitz-Gilbert equation and is used to describe the magnetization
dynamics in a one-dimensional uni-axial ferromagnet. Trough the use of
suitable approximations, we derive the magnetic solitary wave excitations
solutions which have pulse-like shapes. Subsequent numerical simulations
reveal domain wall propagation
Long-range interactions and wave patterns in a DNA model
We propose a spin-like model of DNA nonlinear dynamics with long-range interactions between adjacent base pairs. We show that the model equation is a modified sine-Gordon equation. We perform the linear stability analysis of a plane wave, which predicts high-amplitude and extended oscillating waves for high values of the long-range parameter. This is confirmed numerically and biological implications of the obtained patterns are suggested