1,719 research outputs found
Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal
The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs)
propagating in a dusty plasma crystal is investigated in a continuum
approximation. It is shown that long wavelength LDLWs are modulationally
stable, while shorter wavelengths may be unstable. The possibility for the
formation and propagation of different envelope localized excitations is
discussed. It is shown that the total grain displacement bears a (weak)
constant displacement (zeroth harmonic mode), due to the asymmetric form of the
nonlinear interaction potential. The existence of asymmetric envelope localized
modes is predicted. The types and characteristics of these coherent nonlinear
structures are discussed.Comment: 18 pages, 7 figures, to appear in Physics of Plasma
Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation
We apply a version of the dressing method to a system of four dimensional
nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer
equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform
Method) and nonlinear matrix PDE integrable by the method of characteristics as
particular reductions. Some other reductions are suggested.Comment: 12 page
Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity
Using the numerical solution of the nonlinear Schr\"odinger equation and a
variational method it is shown that (3+1)-dimensional spatiotemporal optical
solitons, known as light bullets, can be stabilized in a layered Kerr medium
with sign-changing nonlinearity along the propagation direction.Comment: 4 pages, 3 PS figure
Instability and Evolution of Nonlinearly Interacting Water Waves
We consider the modulational instability of nonlinearly interacting
two-dimensional waves in deep water, which are described by a pair of
two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear
dispersion relation. The latter is numerically analyzed to obtain the regions
and the associated growth rates of the modulational instability. Furthermore,
we follow the long term evolution of the latter by means of computer
simulations of the governing nonlinear equations and demonstrate the formation
of localized coherent wave envelopes. Our results should be useful for
understanding the formation and nonlinear propagation characteristics of large
amplitude freak waves in deep water.Comment: 4 pages, 4 figures, to appear in Physical Review Letter
Massive Spin-2 fields of Geometric Origin in Curved Spacetimes
We study the consistency of a model which includes torsion as well as the
metric as dynamical fields and has massive spin-2 particle in its spectrum. The
massive spin-2 mode resides in the torsion, rather than in the metric. It is
known that this model is tachyon- and ghost-free in Minkowski background. We
show that this property remains valid and no other pathologies emerge in de
Sitter and anti-de Sitter backgrounds, with some of our results extending to
arbirary Einstein space backgrounds. This suggests that the model is
consistent, at least at the classical level, unlike, e.g., the Fierz--Pauli
theory.Comment: 17 pages, Clarifying remarks added in section 5, minor changes,
version to be published in the Phys. Rev.
A note on the wellposedness of scalar brane world cosmological perturbations
We discuss scalar brane world cosmological perturbations for a 3-brane world
in a maximally symmetric 5D bulk. We show that Mukoyama's master equations
leads, for adiabatic perturbations of a perfect fluid on the brane and for
scalar field matter on the brane, to a well posed problem despite the "non
local" aspect of the boundary condition on the brane. We discuss in relation to
the wellposedness the way to specify initial data in the bulk.Comment: 14 pages, one figure, v2 minor change
Solitary wave interaction in a compact equation for deep-water gravity waves
In this study we compute numerical traveling wave solutions to a compact
version of the Zakharov equation for unidirectional deep-water waves recently
derived by Dyachenko & Zakharov (2011) Furthermore, by means of an accurate
Fourier-type spectral scheme we find that solitary waves appear to collide
elastically, suggesting the integrability of the Zakharov equation.Comment: 8 pages, 5 figures, 23 references. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh/ . arXiv admin note:
text overlap with arXiv:1204.288
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