159 research outputs found
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.
Generation of Intrinsic Vibrational Gap Modes in Three-Dimensional Ionic Crystals
The existence of anharmonic localization of lattice vibrations in a perfect
3-D diatomic ionic crystal is established for the rigid-ion model by molecular
dynamics simulations. For a realistic set of NaI potential parameters, an
intrinsic localized gap mode vibrating in the [111] direction is observed for
fcc and zinc blende lattices. An axial elastic distortion is an integral
feature of this mode which forms more readily for the zinc blende than for the
fcc structure. Molecular dynamics simulations verify that in each structure
this localized mode may be stable for at least 200 cycles.Comment: 5 pages, 4 figures, RevTeX, using epsf.sty. To be published in Phys.
Rev. B. Also available at http://www.msc.cornell.edu/~kiselev
Nonlinear Modulation of Multi-Dimensional Lattice Waves
The equations governing weakly nonlinear modulations of -dimensional
lattices are considered using a quasi-discrete multiple-scale approach. It is
found that the evolution of a short wave packet for a lattice system with cubic
and quartic interatomic potentials is governed by generalized Davey-Stewartson
(GDS) equations, which include mean motion induced by the oscillatory wave
packet through cubic interatomic interaction. The GDS equations derived here
are more general than those known in the theory of water waves because of the
anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations
describing the evolution of long wavelength acoustic modes in two and three
dimensional lattices are also presented. Then the modulational instability of a
-dimensional Stokes lattice wave is discussed based on the -dimensional
GDS equations obtained. Finally, the one- and two-soliton solutions of
two-dimensional GDS equations are provided by means of Hirota's bilinear
transformation method.Comment: Submitted to PR
Breathers on lattices with long range interaction
We analyze the properties of breathers (time periodic spatially localized
solutions) on chains in the presence of algebraically decaying interactions
. We find that the spatial decay of a breather shows a crossover from
exponential (short distances) to algebraic (large distances) decay. We
calculate the crossover distance as a function of and the energy of the
breather. Next we show that the results on energy thresholds obtained for short
range interactions remain valid for and that for (anomalous
dispersion at the band edge) nonzero thresholds occur for cases where the short
range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199
Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity
Nonlinear localized excitations in one-dimensional diatomic lattices with
cubic and quartic nonlinearity are considered analytically by a
quasi-discreteness approach. The criteria for the occurence of asymmetric gap
solitons (with vibrating frequency lying in the gap of phonon bands) and
small-amplitude, asymmetric intrinsic localized modes (with the vibrating
frequency being above all the phonon bands) are obtained explicitly based on
the modulational instabilities of corresponding linear lattice plane waves. The
expressions of particle displacement for all these nonlinear localized
excitations are also given. The result is applied to standard two-body
potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The
comparison with previous numerical study of the anharmonic gap modes in
diatomic lattices for the standard two-body potentials is made and good
agreement is found.Comment: 24 pages in Revtex, 2 PS figure
Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions
We study effects of Kac-Baker long-range dispersive interaction (LRI) between
particles on kink properties in the discrete sine-Gordon model. We show that
the kink width increases indefinitely as the range of LRI grows only in the
case of strong interparticle coupling. On the contrary, the kink becomes
intrinsically localized if the coupling is under some critical value.
Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI
increases for supercritical values of the coupling but remains finite for
subcritical values. We demonstrate that LRI essentially transforms the internal
dynamics of the kinks, specifically creating their internal localized and
quasilocalized modes. We also show that moving kinks radiate plane waves due to
break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.
Solitons in Triangular and Honeycomb Dynamical Lattices with the Cubic Nonlinearity
We study the existence and stability of localized states in the discrete
nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square
lattices. The model includes both the nearest-neighbor and long-range
interactions. For the fundamental strongly localized soliton, the results
depend on the coordination number, i.e., on the particular type of the lattice.
The long-range interactions additionally destabilize the discrete soliton, or
make it more stable, if the sign of the interaction is, respectively, the same
as or opposite to the sign of the short-range interaction. We also explore more
complicated solutions, such as twisted localized modes (TLM's) and solutions
carrying multiple topological charge (vortices) that are specific to the
triangular and honeycomb lattices. In the cases when such vortices are
unstable, direct simulations demonstrate that they turn into zero-vorticity
fundamental solitons.Comment: 17 pages, 13 figures, Phys. Rev.
- …