1,136 research outputs found
Exact Solutions for Domain Walls in Coupled Complex Ginzburg - Landau Equations
The complex Ginzburg Landau equation (CGLE) is a ubiquitous model for the
evolution of slowly varying wave packets in nonlinear dissipative media. A
front (shock) is a transient layer between a plane-wave state and a zero
background. We report exact solutions for domain walls, i.e., pairs of fronts
with opposite polarities, in a system of two coupled CGLEs, which describe
transient layers between semi-infinite domains occupied by each component in
the absence of the other one. For this purpose, a modified Hirota bilinear
operator, first proposed by Bekki and Nozaki, is employed. A novel
factorization procedure is applied to reduce the intermediate calculations
considerably. The ensuing system of equations for the amplitudes and
frequencies is solved by means of computer-assisted algebra. Exact solutions
for mutually-locked front pairs of opposite polarities, with one or several
free parameters, are thus generated. The signs of the cubic gain/loss, linear
amplification/attenuation, and velocity of the coupled-front complex can be
adjusted in a variety of configurations. Numerical simulations are performed to
study the stability properties of such fronts.Comment: Journal of the Physical Society of Japan, in pres
generating technique for minimal D=5 supergravity and black rings
A solution generating technique is developed for D=5 minimal supergravity
with two commuting Killing vectors based on the U-duality arising in the
reduction of the theory to three dimensions. The target space of the
corresponding 3-dimensional sigma-model is the coset . Its isometries constitute the set of solution generating symmetries.
These include two electric and two magnetic Harrison transformations with the
corresponding two pairs of gauge transformations, three -duality
transformations, and the three gravitational scale, gauge and Ehlers
transformations (altogether 14). We construct a representation of the coset in
terms of matrices realizing the automorphisms of split octonions.
Generating a new solution amounts to transforming the coset matrices by
one-parametric subgroups of and subsequently solving the dualization
equations. Using this formalism we derive a new charged black ring solution
with two independent parameters of rotation.Comment: 21 pages revtex-4, 1 figure, typo corrected in Eq. (103
Contributions of plasma physics to chaos and nonlinear dynamics
This topical review focusses on the contributions of plasma physics to chaos
and nonlinear dynamics bringing new methods which are or can be used in other
scientific domains. It starts with the development of the theory of Hamiltonian
chaos, and then deals with order or quasi order, for instance adiabatic and
soliton theories. It ends with a shorter account of dissipative and high
dimensional Hamiltonian dynamics, and of quantum chaos. Most of these
contributions are a spin-off of the research on thermonuclear fusion by
magnetic confinement, which started in the fifties. Their presentation is both
exhaustive and compact. [15 April 2016
Signatures of chaotic tunnelling
Recent experiments with cold atoms provide a significant step toward a better
understanding of tunnelling when irregular dynamics is present at the classical
level. In this paper, we lay out numerical studies which shed light on the
previous experiments, help to clarify the underlying physics and have the
ambition to be guidelines for future experiments.Comment: 11 pages, 9 figures, submitted to Phys. Rev. E. Figures of better
quality can be found at http://www.phys.univ-tours.fr/~mouchet
Reduction of dimension for nonlinear dynamical systems
We consider reduction of dimension for nonlinear dynamical systems. We
demonstrate that in some cases, one can reduce a nonlinear system of equations
into a single equation for one of the state variables, and this can be useful
for computing the solution when using a variety of analytical approaches. In
the case where this reduction is possible, we employ differential elimination
to obtain the reduced system. While analytical, the approach is algorithmic,
and is implemented in symbolic software such as {\sc MAPLE} or {\sc SageMath}.
In other cases, the reduction cannot be performed strictly in terms of
differential operators, and one obtains integro-differential operators, which
may still be useful. In either case, one can use the reduced equation to both
approximate solutions for the state variables and perform chaos diagnostics
more efficiently than could be done for the original higher-dimensional system,
as well as to construct Lyapunov functions which help in the large-time study
of the state variables. A number of chaotic and hyperchaotic dynamical systems
are used as examples in order to motivate the approach.Comment: 16 pages, no figure
On the localized wave patterns supported by convection-reaction-diffusion equation
A set of traveling wave solution to convection-reaction-diffusion equation is
studied by means of methods of local nonlinear analysis and numerical
simulation. It is shown the existence of compactly supported solutions as well
as solitary waves within this family for wide range of parameter values
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