276 research outputs found
Moving Embedded Solitons
The first theoretical results are reported predicting {\em moving} solitons
residing inside ({\it embedded} into) the continuous spectrum of radiation
modes. The model taken is a Bragg-grating medium with Kerr nonlinearity and
additional second-derivative (wave) terms. The moving embedded solitons (ESs)
are doubly isolated (of codimension 2), but, nevertheless, structurally stable.
Like quiescent ESs, moving ESs are argued to be stable to linear approximation,
and {\it semi}-stable nonlinearly. Estimates show that moving ESs may be
experimentally observed as 10 fs pulses with velocity th that
of light.Comment: 9 pages 2 figure
Embedded Solitons in a Three-Wave System
We report a rich spectrum of isolated solitons residing inside ({\it embedded
} into) the continuous radiation spectrum in a simple model of three-wave
spatial interaction in a second-harmonic-generating planar optical waveguide
equipped with a quasi-one-dimensional Bragg grating. An infinite sequence of
fundamental embedded solitons are found, which differ by the number of internal
oscillations. Branches of these zero-walkoff spatial solitons give rise,
through bifurcations, to several secondary branches of walking solitons. The
structure of the bifurcating branches suggests a multistable configuration of
spatial optical solitons, which may find straightforward applications for
all-optical switching.Comment: 5 pages 5 figures. To appear in Phys Rev
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Factors affecting distribution and habitat selection of water shrews Neomys fodiens
The water shrew Neomys fodiens is one of Britain’s least known mammals and its habitat requirements are poorly understood. The purpose of this study was to determine occurrence and associated habitat preferences of water shrews, a species of conservation concern, by comparing populations in central England freshwater habitats. Bait tube surveys were undertaken at 32 freshwater sites to establish water shrew presence, half of which were found to contain water shrews. Habitat surveys were undertaken and, in addition to water shrew presence/absence data, were used to develop habitat suitability index models by means of artificial neural networks. Management intensity (occasional or frequent bankside management) was identified as the most important predictor of water shrew presence and, when combined with dissolved oxygen (0-2.99mg l-1) and water depth (<25cm), created the highest performing model. These models will allow sites to be rapidly assessed for water shrew presence without labour intensive and costly live-trapping techniques. Prey availability was investigated by undertaking invertebrate surveys at four water shrew-positive sites, as well as at an additional four sites with unknown water shrew presence with which to compare
Thirring Solitons in the presence of dispersion
The effect of dispersion or diffraction on zero-velocity solitons is studied
for the generalized massive Thirring model describing a nonlinear optical fiber
with grating or parallel-coupled planar waveguides with misaligned axes. The
Thirring solitons existing at zero dispersion/diffraction are shown numerically
to be separated by a finite gap from three isolated soliton branches. Inside
the gap, there is an infinity of multi-soliton branches. Thus, the Thirring
solitons are structurally unstable. In another parameter region (far from the
Thirring limit), solitons exist everywhere.Comment: 12 pages, Latex. To appear in Phys. Rev. Let
Embedded Solitons in Lagrangian and Semi-Lagrangian Systems
We develop the technique of the variational approximation for solitons in two
directions. First, one may have a physical model which does not admit the usual
Lagrangian representation, as some terms can be discarded for various reasons.
For instance, the second-harmonic-generation (SHG) model considered here, which
includes the Kerr nonlinearity, lacks the usual Lagrangian representation if
one ignores the Kerr nonlinearity of the second harmonic, as compared to that
of the fundamental. However, we show that, with a natural modification, one may
still apply the variational approximation (VA) to those seemingly flawed
systems as efficiently as it applies to their fully Lagrangian counterparts. We
call such models, that do not admit the usual Lagrangian representation,
\textit{semi-Lagrangian} systems. Second, we show that, upon adding an
infinitesimal tail that does not vanish at infinity, to a usual soliton ansatz,
one can obtain an analytical criterion which (within the framework of VA) gives
a condition for finding \textit{embedded solitons}, i.e., isolated truly
localized solutions existing inside the continuous spectrum of the radiation
modes. The criterion takes a form of orthogonality of the radiation mode in the
infinite tail to the soliton core. To test the criterion, we have applied it to
both the semi-Lagrangian truncated version of the SHG model and to the same
model in its full form. In the former case, the criterion (combined with VA for
the soliton proper) yields an \emph{exact} solution for the embedded soliton.
In the latter case, the criterion selects the embedded soliton with a relative
error .Comment: 10 pages, 1 figur
Radiationless Travelling Waves In Saturable Nonlinear Schr\"odinger Lattices
The longstanding problem of moving discrete solitary waves in nonlinear
Schr{\"o}dinger lattices is revisited. The context is photorefractive crystal
lattices with saturable nonlinearity whose grand-canonical energy barrier
vanishes for isolated coupling strength values. {\em Genuinely localised
travelling waves} are computed as a function of the system parameters {\it for
the first time}. The relevant solutions exist only for finite velocities.Comment: 5 pages, 4 figure
Origin of Multikinks in Dispersive Nonlinear Systems
We develop {\em the first analytical theory of multikinks} for strongly {\em
dispersive nonlinear systems}, considering the examples of the weakly discrete
sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise
parabolic potential. We reveal that there are no -kinks for this model,
but there exist {\em discrete sets} of -kinks for all N>1. We also show
their bifurcation structure in driven damped systems.Comment: 4 pages 5 figures. To appear in Phys Rev
Stripe to spot transition in a plant root hair initiation model
A generalised Schnakenberg reaction-diffusion system with source and loss
terms and a spatially dependent coefficient of the nonlinear term is studied
both numerically and analytically in two spatial dimensions. The system has
been proposed as a model of hair initiation in the epidermal cells of plant
roots. Specifically the model captures the kinetics of a small G-protein ROP,
which can occur in active and inactive forms, and whose activation is believed
to be mediated by a gradient of the plant hormone auxin. Here the model is made
more realistic with the inclusion of a transverse co-ordinate. Localised
stripe-like solutions of active ROP occur for high enough total auxin
concentration and lie on a complex bifurcation diagram of single and
multi-pulse solutions. Transverse stability computations, confirmed by
numerical simulation show that, apart from a boundary stripe, these 1D
solutions typically undergo a transverse instability into spots. The spots so
formed typically drift and undergo secondary instabilities such as spot
replication. A novel 2D numerical continuation analysis is performed that shows
the various stable hybrid spot-like states can coexist. The parameter values
studied lead to a natural singularly perturbed, so-called semi-strong
interaction regime. This scaling enables an analytical explanation of the
initial instability, by describing the dispersion relation of a certain
non-local eigenvalue problem. The analytical results are found to agree
favourably with the numerics. Possible biological implications of the results
are discussed.Comment: 28 pages, 44 figure
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