53 research outputs found
Effects of finite curvature on soliton dynamics in a chain of nonlinear oscillators
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 decreases when curvature increases, i.e. bending manifests
itself as a trap for excitations. Moreover, the potential of this trap is
double-well, thus leading to a symmetry breaking phenomenon: a symmetric
stationary state may become unstable and transform into an energetically
favorable asymmetric stationary state. The essentials of symmetry breaking are
examined analytically for a simplified model. We also demonstrate a threshold
character of the scattering process, i.e. transmission, trapping, or reflection
of the moving nonlinear excitation passing through the bending.Comment: 13 pages (LaTeX) with 10 figures (EPS
Models for energy and charge transport and storage in biomolecules
Two models for energy and charge transport and storage in biomolecules are
considered. A model based on the discrete nonlinear Schrodinger equation with
long-range dispersive interactions (LRI's) between base pairs of DNA is offered
for the description of nonlinear dynamics of the DNA molecule. We show that
LRI's are responsible for the existence of an interval of bistability where two
stable stationary states, a narrow, pinned state and a broad, mobile state,
coexist at each value of the total energy. The possibility of controlled
switching between pinned and mobile states is demonstrated. The mechanism could
be important for controlling energy storage and transport in DNA molecules.
Another model is offered for the description of nonlinear excitations in
proteins and other anharmonic biomolecules. We show that in the highly
anharmonic systems a bound state of Davydov and Boussinesq solitons can exist.Comment: 12 pages (latex), 12 figures (ps
Solitons in anharmonic chains with ultra-long-range interatomic interactions
We study the influence of long-range interatomic interactions on the
properties of supersonic pulse solitons in anharmonic chains. We show that in
the case of ultra-long-range (e.g., screened Coulomb) interactions three
different types of pulse solitons coexist in a certain velocity interval: one
type is unstable but the two others are stable. The high-energy stable soliton
is broad and can be described in the quasicontinuum approximation. But the
low-energy stable soliton consists of two components, short-range and
long-range ones, and can be considered as a bound state of these components.Comment: 4 pages (LaTeX), 5 figures (Postscript); submitted to Phys. Rev.
Multi-soliton energy transport in anharmonic lattices
We demonstrate the existence of dynamically stable multihump solitary waves
in polaron-type models describing interaction of envelope and lattice
excitations. In comparison with the earlier theory of multihump optical
solitons [see Phys. Rev. Lett. {\bf 83}, 296 (1999)], our analysis reveals a
novel physical mechanism for the formation of stable multihump solitary waves
in nonintegrable multi-component nonlinear models.Comment: 4 pages, 4 figure
- …