423 research outputs found
The 4-beaches survey in Uganda: Nkombe Beach
This paper analyses the location, potentialities and set-backs of Nkombe Beach, the landing site chosen in Uganda for the 4-beaches survey
Spatial solitons in a medium composed of self-focusing and self-defocusing layers
We introduce a model combining Kerr nonlinearity with a periodically changing
sign ("nonlinearity management") and a Bragg grating (BG). The main result,
obtained by means of systematic simulations, is presented in the form of a
soliton's stability diagram on the parameter plane of the model; the diagram
turns out to be a universal one, as it practically does not depend on the
soliton's power. Moreover, simulations of the nonlinear Schroedinger (NLS)
model subjected to the same "nonlinearity management" demonstrate that the same
diagram determines the stability of the NLS solitons, unless they are very
narrow. The stability region of very narrow NLS solitons is much smaller, and
soliton splitting is readily observed in that case. The universal diagram shows
that a minimum non-zero average value of the Kerr coefficient is necessary for
the existence of stable solitons. Interactions between identical solitons with
an initial phase difference between them are simulated too in the BG model,
resulting in generation of stable moving solitons. A strong spontaneous
symmetry breaking is observed in the case when in-phase solitons pass through
each other due to attraction between them.Comment: a latex text file and 9 eps files with figures. Physics Letters A, in
pres
The Jinja Stakeholders' Workshop, February 21st -23rd, 2001
This book section is a review of a workshop, the one held at Jinja in Uganda, which aimed to assess the potential local stakeholders within the frame of the co-management of Lake Victoria's fisheries
Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system
A system consisting of the cubic complex Ginzburg-Landau equation which is
linearly coupled to an additional linear dissipative equation, is considered.
The model was introduced earlier in the context of dual-core nonlinear optical
fibers with one active and one passive cores. We argue that it may also
possibly describe traveling-wave convection in a channel with an inner vertical
partition. By means of systematic simulations, we find new types of stable
localized excitations, which exist in the system in addition to the earlier
found stationary pulses. The new localized excitations include pulses existing
on top of a small-amplitude background (that may be regular or chaotic) {\em
above} the threshold of instability of the zero solution, and breathers into
which stationary pulses are transformed through a Hopf bifurcation below the
zero-solution instability threshold. A sharp border between the stable
stationary pulses and breathers, precluding their coexistence, is identified.
Stable bound states of two breathers with a phase shift between their
internal vibrations are found too. Above the threshold, the pulses are standing
if the small-amplitude background oscillations are regular; if the background
is chaotic, the pulses are randomly walking. With the increase of the system's
size, more randomly walking pulses are spontaneously generated. The random walk
of different pulses in a multi-pulse state is synchronized (but not completely)
due to their mutual repulsion. At a large overcriticality, the multi-pulse
state goes over into a spatiotemporal chaos.Comment: 16page,12figure
Stable solitons in coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities
We introduce a model of a two-core system, based on an equation of the
Ginzburg-Landau (GL) type, coupled to another GL equation, which may be linear
or nonlinear. One core is active, featuring intrinsic linear gain, while the
other one is lossy. The difference from previously studied models involving a
pair of linearly coupled active and passive cores is that the stabilization of
the system is provided not by a linear diffusion-like term, but rather by a
cubic or quintic dissipative term in the active core. Physical realizations of
the models include systems from nonlinear optics (semiconductor waveguides or
optical cavities), and a double-cigar-shaped Bose-Einstein condensate with a
negative scattering length, in which the active ``cigar'' is an atom laser. The
replacement of the diffusion term by the nonlinear loss is principally
important, as diffusion does not occur in these physical media, while nonlinear
loss is possible. A stability region for solitary pulses is found in the
system's parameter space by means of direct simulations. One border of the
region is also found in an analytical form by means of a perturbation theory.
Moving pulses are studied too. It is concluded that collisions between them are
completely elastic, provided that the relative velocity is not too small. The
pulses withstand multiple tunneling through potential barriers. Robust
quantum-rachet regimes of motion of the pulse in a time-periodic asymmetric
potential are found as well.Comment: 14 pages, 7 figure
Stable autosolitons in dispersive media with saturable gain and absorption
We introduce the simplest one-dimensional model of a dispersive optical
medium with saturable dissipative nonlinearity and filtering (dispersive loss)
which gives rise to stable solitary pulses (autosolitons). In the particular
case when the dispersive loss is absent, the same model may also be interpreted
as describing a stationary field in a planar optical waveguide with uniformly
distributed saturable gain and absorption. In a certain region of the model's
parameter space, two coexisting solitary-pulse solutions are found numerically,
one of which may be stable. Solving the corresponding linearized eigenvalue
problem, we identify stability borders for the solitary pulses in their
parametric plane. Beyond one of the borders, the symmetric pulse is destroyed
by asymmetric perturbations, and at the other border it undergoes a Hopf
bifurcation, which may turn it into a breather.Comment: A latex text file and four ps files with figures. Physics Letters A,
in pres
On integers for which the sum of divisors is the square of the squarefree core
We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four distinct prime factors is n = 1782. We show that there is no solution which is fourth power free. We also show that the number of solutions up to x > 1 is at most x ⅟⁴⁺ᵉ for any ε > 0 and all x > xε. Further, call n primitive if no proper unitary divisor d of n satisfies σ(d) | γ(d) ² . We show that the number of primitive solutions to the equation up to x is less than xᵉ for x > xₑ
Stability and interactions of solitons in two-component active systems
We demonstrate that solitary pulses in linearly coupled nonlinear Schrödinger equations with gain in one mode and losses in another one, which is a model of an asymmetric erbium-doped nonlinear optical coupler, exist and are stable, as was recently predicted analytically. Next, we consider interactions between the pulses. The in-phase pulses attract each other and merge into a single one. Numerical and analytical consideration of the repulsive interaction between π-out-of-phase pulses reveals the existence of their robust pseudobound state, when a final separation between them takes an almost constant minimum value, as a function of the initial separation, Tin, in a certain interval of Tin. In the case of the phase difference π/2, the interaction is also repulsive. © 1996 The American Physical Society
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