2,738 research outputs found
Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation
We obtain exact moving and stationary, spatially periodic and localized
solutions of a generalized discrete nonlinear Schr\"odinger equation. More
specifically, we find two different moving periodic wave solutions and a
localized moving pulse solution. We also address the problem of finding exact
stationary solutions and, for a particular case of the model when stationary
solutions can be expressed through the Jacobi elliptic functions, we present a
two-point map from which all possible stationary solutions can be found.
Numerically we demonstrate the generic stability of the stationary pulse
solutions and also the robustness of moving pulses in long-term dynamics.Comment: 22 pages, 7 figures, to appear in J. Phys.
Properties of discrete breathers in graphane from ab initio simulations
A density functional theory (DFT) study of the discrete breathers (DBs) in
graphane (fully hydrogenated graphene) was performed. To the best of our
knowledge, this is the first demonstration of the existence of DBs in a
crystalline body from the first-principle simulations. It is found that the DB
is a robust, highly localized vibrational mode with one hydrogen atom
oscillating with a large amplitude along the direction normal to the graphane
plane with all neighboring atoms having much smaller vibration amplitudes. DB
frequency decreases with increase in its amplitude, and it can take any value
within the phonon gap and can even enter the low-frequency phonon band. The
concept of DB is then used to propose an explanation to the recent experimental
results on the nontrivial kinetics of graphane dehydrogenation at elevated
temperatures.Comment: 20.07.14 Submitted to PhysRev
Translationally invariant nonlinear Schrodinger lattices
Persistence of stationary and traveling single-humped localized solutions in
the spatial discretizations of the nonlinear Schrodinger (NLS) equation is
addressed. The discrete NLS equation with the most general cubic polynomial
function is considered. Constraints on the nonlinear function are found from
the condition that the second-order difference equation for stationary
solutions can be reduced to the first-order difference map. The discrete NLS
equation with such an exceptional nonlinear function is shown to have a
conserved momentum but admits no standard Hamiltonian structure. It is proved
that the reduction to the first-order difference map gives a sufficient
condition for existence of translationally invariant single-humped stationary
solutions and a necessary condition for existence of single-humped traveling
solutions. Other constraints on the nonlinear function are found from the
condition that the differential advance-delay equation for traveling solutions
admits a reduction to an integrable normal form given by a third-order
differential equation. This reduction also gives a necessary condition for
existence of single-humped traveling solutions. The nonlinear function which
admits both reductions defines a two-parameter family of discrete NLS equations
which generalizes the integrable Ablowitz--Ladik lattice.Comment: 24 pages, 4 figure
AC Josephson properties of phase slip lines in wide tin films
Current steps in the current-voltage characteristics of wide superconducting
Sn films exposed to a microwave irradiation were observed in the resistive
state with phase slip lines. The behaviour of the magnitude of the steps on the
applied irradiation power was found to be similar to that for the current steps
in narrow superconducting channels with phase slip centers and, to some extent,
for the Shapiro steps in Josephson junctions. This provides evidence for the
Josephson properties of the phase slip lines in wide superconducting films and
supports the assumption about similarity between the processes of phase slip in
wide and narrow films.Comment: 7 pages, 2 figures, to be published in Supercond. Sci. Techno
Nonlinear Lattices Generated from Harmonic Lattices with Geometric Constraints
Geometrical constraints imposed on higher dimensional harmonic lattices
generally lead to nonlinear dynamical lattice models. Helical lattices obtained
by such a procedure are shown to be described by sine- plus linear-lattice
equations. The interplay between sinusoidal and quadratic potential terms in
such models is shown to yield localized nonlinear modes identified as intrinsic
resonant modes
Kinks in dipole chains
It is shown that the topological discrete sine-Gordon system introduced by
Speight and Ward models the dynamics of an infinite uniform chain of electric
dipoles constrained to rotate in a plane containing the chain. Such a chain
admits a novel type of static kink solution which may occupy any position
relative to the spatial lattice and experiences no Peierls-Nabarro barrier.
Consequently the dynamics of a single kink is highly continuum like, despite
the strongly discrete nature of the model. Static multikinks and kink-antikink
pairs are constructed, and it is shown that all such static solutions are
unstable. Exact propagating kinks are sought numerically using the
pseudo-spectral method, but it is found that none exist, except, perhaps, at
very low speed.Comment: Published version. 21 pages, 5 figures. Section 3 completely
re-written. Conclusions unchange
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