1,511 research outputs found
Transverse Patterns in Nonlinear Optical Resonators
The book is devoted to the formation and dynamics of localized structures
(vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in
nonlinear optical resonators such as lasers, optical parametric oscillators,
and photorefractive oscillators. The theoretical analysis is performed by
deriving order parameter equations, and also through numerical integration of
microscopic models of the systems under investigation. Experimental
observations, and possible technological implementations of transverse optical
patterns are also discussed. A comparison with patterns found in other
nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is
given. This article contains the table of contents and the introductory chapter
of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of
the boo
Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
We consider the three-dimensional (3D) mean-field model for the Bose-Einstein
condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes
the sign of the nonlinearity along the axial direction, and the
harmonic-oscillator trapping potential applied in the transverse plane. The
lattice can be created as an optical or magnetic one, by means of available
experimental techniques. The objective is to identify stable 3D solitons
supported by the setting. Two methods are developed for this purpose: The
variational approximation, formulated in the framework of the 3D
Gross-Pitaevskii equation, and the 1D nonpolynomial Schr\"{o}dinger equation
(NPSE) in the axial direction, which allows one to predict the collapse in the
framework of the 1D description. Results are summarized in the form of a
stability region for the solitons in the plane of the NL strength and
wavenumber. Both methods produce a similar form of the stability region. Unlike
their counterparts supported by the NL in the 1D model with the cubic
nonlinearity, kicked solitons of the NPSE cannot be set in motion, but the kick
may help to stabilize them against the collapse, by causing the solitons to
shed excess norm. A dynamical effect specific to the NL is found in the form of
freely propagating small-amplitude wave packets emitted by perturbed solitons.Comment: 14 pages, 8 figures. To be published in J. Phys. B: At. Mol. Opt.
Phy
Robust ultrashort light bullets in strongly twisted waveguide arrays
We introduce a new class of stable light bullets that form in twisted waveguide arrays pumped with ultrashort pulses, where twisting offers a powerful knob to tune the properties of localized states. We find that, above a critical twist, three-dimensional wave packets are unambiguously stabilized, with no minimum energy threshold. As a consequence, when the higher-order perturbations that accompany ultrashort pulse propagation are at play, the bullets dynamically adjust and sweep along stable branches. Therefore, they are predicted to feature an unprecedented experimental robustness.Peer ReviewedPostprint (published version
Effect of noise on coupled chaotic systems
Effect of noise in inducing order on various chaotically evolving systems is
reviewed, with special emphasis on systems consisting of coupled chaotic
elements. In many situations it is observed that the uncoupled elements when
driven by identical noise, show synchronization phenomena where chaotic
trajectories exponentially converge towards a single noisy trajectory,
independent of the initial conditions. In a random neural network, with
infinite range coupling, chaos is suppressed due to noise and the system
evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon
has been observed in a square array of coupled threshold devices where a
temporal characteristic of the system resonates at a given noise strength. In a
chaotically evolving coupled map lattice with logistic map as local dynamics
and driven by identical noise at each site, we report that the number of
structures (a structure is a group of neighbouring lattice sites for whom
values of the variable follow certain predefined pattern) follow a power-law
decay with the length of the structure. An interesting phenomenon, which we
call stochastic coherence, is also reported in which the abundance and
lifetimes of these structures show characteristic peaks at some intermediate
noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure
Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
The aim of the present review is to introduce the reader to some of the
physical notions and of the mathematical methods that are relevant to the study
of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the
general framework, we discuss the prototypical models that are relevant to this
setting for different dimensions and different potentials confining the atoms.
We analyze some of the model properties and explore their typical wave
solutions (plane wave solutions, bright, dark, gap solitons, as well as
vortices). We then offer a collection of mathematical methods that can be used
to understand the existence, stability and dynamics of nonlinear waves in such
BECs, either directly or starting from different types of limits (e.g., the
linear or the nonlinear limit, or the discrete limit of the corresponding
equation). Finally, we consider some special topics involving more recent
developments, and experimental setups in which there is still considerable need
for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new
references added, fixed typo
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