535 research outputs found
Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization
Exact stationary soliton solutions of the fifth order KdV type equation are obtained for any p
() in case , , (where D is the
soliton velocity), and it is shown that these solutions are unstable with
respect to small perturbations in case . Various properties of these
solutions are discussed. In particular, it is shown that for any p, these
solitons are lower and narrower than the corresponding solitons.
Finally, for p = 2 we obtain an exact stationary soliton solution even when
are all and discuss its various properties.Comment: 8 pages, no figure
Locking the Golden Door and Throwing Away the Key: An Analysis of Asylum during the Years of the Trump Administration
The years of the Trump Administration have certainly been some of the most divisive in modern American political history. One of the largest divides arose from former President Trump’s brazen, “zero tolerance” immigration policies that relentlessly attacked many forms of immigration coming into the United States. Asylum-based immigration, which allows immigrants to come to this country as a safe haven when they are fleeing persecution in their home countries, was one of former President Trump’s main targets. Former President Trump even came dangerously close to eliminating asylum-based immigration with his “Death to Asylum” policy in December of 2020. President Biden has since reversed many of former President Trump’s detrimental asylum policies and enacted executive orders that facilitate asylum-based immigration. While asylum-based immigration has been saved by President Biden (for now), the actions of the Trump Administration have highlighted the issues regarding lack of consistency and over-delegation to the executive branch that plague immigration law to this day. This Note will examine various sources of asylum law, both prior to and during the Trump Administration, and evaluate the constitutionality of asylum policies between 2016 and 2020. Finally, this Note will give four recommendations future administrations can implement in order to provide fairer and more consistent asylum policies that are not so dependent on which President happens to be in power at the time: (1) creating a direct, fair, and inclusive path to citizenship; (2) decreasing ICE’s role in exchange for increasing the EOIR’s presence; (3) changing the focus in creating available facilities to immigrants; and (4) guaranteeing legal representation in immigration proceedings
Scattering and Trapping of Nonlinear Schroedinger Solitons in External Potentials
Soliton motion in some external potentials is studied using the nonlinear
Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons
propagate almost freely or are trapped in a periodic potential. The critical
kinetic energy for reflection and trapping is evaluated approximately with a
variational method.Comment: 9 pages, 7 figure
Chaotic behaviour of nonlinear waves and solitons of perturbed Korteweg - de Vries equation
This paper considers properties of nonlinear waves and solitons of
Korteweg-de Vries equation in the presence of external perturbation. For
time-periodic hamiltonian perturbation the width of the stochastic layer is
calculated. The conclusions about chaotic behaviour in long-period waves and
solitons are inferred. Obtained theoretical results find experimental
confirmation in experiments with the propagation of ion-acoustic waves in
plasma.Comment: 7 pages, LaTeX, 2 Postscript figures, submitted to Reports on
Mathematical Physic
Nonlinear Schr\"odinger Equation with Spatio-Temporal Perturbations
We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger
Equation (NLSE) with the following perturbations: non-parametric
spatio-temporal driving of the form , damping, and a
linear term which serves to stabilize the driven soliton. Using the time
evolution of norm, momentum and energy, or, alternatively, a Lagrangian
approach, we develop a Collective-Coordinate-Theory which yields a set of ODEs
for our four collective coordinates. These ODEs are solved analytically and
numerically for the case of a constant, spatially periodic force . The
soliton position exhibits oscillations around a mean trajectory with constant
velocity. This means that the soliton performs, on the average, a
unidirectional motion although the spatial average of the force vanishes. The
amplitude of the oscillations is much smaller than the period of . In
order to find out for which regions the above solutions are stable, we
calculate the time evolution of the soliton momentum and soliton
velocity : This is a parameter representation of a curve which is
visited by the soliton while time evolves. Our conjecture is that the soliton
becomes unstable, if this curve has a branch with negative slope. This
conjecture is fully confirmed by our simulations for the perturbed NLSE.
Moreover, this curve also yields a good estimate for the soliton lifetime: the
soliton lives longer, the shorter the branch with negative slope is.Comment: 21 figure
Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability
We show that the phenomenon of modulational instability in arrays of
Bose-Einstein condensates confined to optical lattices gives rise to coherent
spatial structures of localized excitations. These excitations represent thin
disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with
condensed atoms of much greater density compared to surrounding array sites.
Aspects of the developed pattern depend on the initial distribution function of
the condensate over the optical lattice, corresponding to particular points of
the Brillouin zone. The long-time behavior of the spatial structures emerging
due to modulational instability is characterized by the periodic recurrence to
the initial low-density state in a finite optical lattice. We propose a simple
way to retain the localized spatial structures with high atomic concentration,
which may be of interest for applications. Theoretical model, based on the
multiple scale expansion, describes the basic features of the phenomenon.
Results of numerical simulations confirm the analytical predictions.Comment: 17 pages, 13 figure
New features of modulational instability of partially coherent light; importance of the incoherence spectrum
It is shown that the properties of the modulational instability of partially
coherent waves propagating in a nonlinear Kerr medium depend crucially on the
profile of the incoherent field spectrum. Under certain conditions, the
incoherence may even enhance, rather than suppress, the instability. In
particular, it is found that the range of modulationally unstable wave numbers
does not necessarily decrease monotonously with increasing degree of
incoherence and that the modulational instability may still exist even when
long wavelength perturbations are stable.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Singularites in the Bousseneq equation and in the generalized KdV equation
In this paper, two kinds of the exact singular solutions are obtained by the
improved homogeneous balance (HB) method and a nonlinear transformation. The
two exact solutions show that special singular wave patterns exists in the
classical model of some nonlinear wave problems
Shock waves in the dissipative Toda lattice
We consider the propagation of a shock wave (SW) in the damped Toda lattice.
The SW is a moving boundary between two semi-infinite lattice domains with
different densities. A steadily moving SW may exist if the damping in the
lattice is represented by an ``inner'' friction, which is a discrete analog of
the second viscosity in hydrodynamics. The problem can be considered
analytically in the continuum approximation, and the analysis produces an
explicit relation between the SW's velocity and the densities of the two
phases. Numerical simulations of the lattice equations of motion demonstrate
that a stable SW establishes if the initial velocity is directed towards the
less dense phase; in the opposite case, the wave gradually spreads out. The
numerically found equilibrium velocity of the SW turns out to be in a very good
agreement with the analytical formula even in a strongly discrete case. If the
initial velocity is essentially different from the one determined by the
densities (but has the correct sign), the velocity does not significantly
alter, but instead the SW adjusts itself to the given velocity by sending
another SW in the opposite direction.Comment: 10 pages in LaTeX, 5 figures available upon regues
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
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