902 research outputs found

### Boundary effects on localized structures in spatially extended systems

We present a general method of analyzing the influence of finite size and
boundary effects on the dynamics of localized solutions of non-linear spatially
extended systems. The dynamics of localized structures in infinite systems
involve solvability conditions that require projection onto a Goldstone mode.
Our method works by extending the solvability conditions to finite sized
systems, by incorporating the finite sized modifications of the Goldstone mode
and associated nonzero eigenvalue. We apply this method to the special case of
non-equilibrium domain walls under the influence of Dirichlet boundary
conditions in a parametrically forced complex Ginzburg Landau equation, where
we examine exotic nonuniform domain wall motion due to the influence of
boundary conditions.Comment: 9 pages, 5 figures, submitted to Physical Review

### Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane

We present a new vorticity-raising transformation for the second integrable
complexification of the sine-Gordon equation on the plane. The new
transformation is a product of four Schlesinger maps of the Painlev\'{e}-V to
itself, and allows a more efficient construction of the $n$-vortex solution
than the previously reported transformation comprising a product of $2n$ maps.Comment: Part of a talk given at a conference on "Nonlinear Physics. Theory
and Experiment", Gallipoli (Lecce), June-July 2004. To appear in a topical
issue of "Theoretical and Mathematical Physics". 7 pages, 1 figur

### Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation

We construct exact localised solutions of the PT-symmetric Gross-Pitaevskii
equation with an attractive cubic nonlinearity. The trapping potential has the
form of two $\delta$-function wells, where one well loses particles while the
other one is fed with atoms at an equal rate. The parameters of the constructed
solutions are expressible in terms of the roots of a system of two
transcendental algebraic equations. We also furnish a simple analytical
treatment of the linear Schr\"odinger equation with the PT-symmetric
double-$\delta$ potential.Comment: To appear in Proceedings of the 15 Conference on Pseudo-Hermitian
Hamiltonians in Quantum Physics, May 18-23 2015, Palermo, Italy (Springer
Proceedings in Physics, 2016

### Einstein-Infeld-Hoffman method and soliton dynamics in a parity noninvariant system

We consider slow motion of a pointlike topological defect (vortex) in the
nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field
and subject to external uniform magnetic field. It turns out that a formal
expansion of fields in powers of defect velocity yields only the trivial static
solution. To obtain a nontrivial solution one has to treat velocities and
accelerations as being of the same order. We assume that acceleration is a
linear form of velocity. The field equations linearized in velocity uniquely
determine the linear relation. It turns out that the only nontrivial solution
is the cyclotron motion of the vortex together with the whole condensate. This
solution is a perturbative approximation to the center of mass motion known
from the theory of magnetic translations.Comment: 6 pages in Latex; shortened version to appear in Phys.Rev.

### Exact vortex solutions of the complex sine-Gordon theory on the plane

We construct explicit multivortex solutions for the first and second complex
sine-Gordon equations. The constructed solutions are expressible in terms of
the modified Bessel and rational functions, respectively. The vorticity-raising
and lowering Backlund transformations are interpreted as the Schlesinger
transformations of the fifth Painleve equation.Comment: 10 pages, 1 figur

### Resonantly driven wobbling kinks

The amplitude of oscillations of the freely wobbling kink in the $\phi^4$
theory decays due to the emission of second-harmonic radiation. We study the
compensation of these radiation losses (as well as additional dissipative
losses) by the resonant driving of the kink. We consider both direct and
parametric driving at a range of resonance frequencies. In each case, we derive
the amplitude equations which describe the evolution of the amplitude of the
wobbling and the kink's velocity. These equations predict multistability and
hysteretic transitions in the wobbling amplitude for each driving frequency --
the conclusion verified by numerical simulations of the full partial
differential equation. We show that the strongest parametric resonance occurs
when the driving frequency equals the natural wobbling frequency and not double
that value. For direct driving, the strongest resonance is at half the natural
frequency, but there is also a weaker resonance when the driving frequency
equals the natural wobbling frequency itself. We show that this resonance is
accompanied by translational motion of the kink.Comment: 19 pages in a double-column format; 8 figure

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