1,322 research outputs found
PT-symmetric sine-Gordon breathers
In this work, we explore a prototypical example of a genuine continuum
breather (i.e., not a standing wave) and the conditions under which it can
persist in a -symmetric medium. As our model of interest, we
will explore the sine-Gordon equation in the presence of a -
symmetric perturbation. Our main finding is that the breather of the
sine-Gordon model will only persist at the interface between gain and loss that
-symmetry imposes but will not be preserved if centered at the
lossy or at the gain side. The latter dynamics is found to be interesting in
its own right giving rise to kink-antikink pairs on the gain side and complete
decay of the breather on the lossy side. Lastly, the stability of the breathers
centered at the interface is studied. As may be anticipated on the basis of
their "delicate" existence properties such breathers are found to be
destabilized through a Hopf bifurcation in the corresponding Floquet analysis
Pattern formation and localization in the forced-damped FPU lattice
We study spatial pattern formation and energy localization in the dynamics of
an anharmonic chain with quadratic and quartic intersite potential subject to
an optical, sinusoidally oscillating field and a weak damping. The
zone-boundary mode is stable and locked to the driving field below a critical
forcing that we determine analytically using an approximate model which
describes mode interactions. Above such a forcing, a standing modulated wave
forms for driving frequencies below the band-edge, while a ``multibreather''
state develops at higher frequencies. Of the former, we give an explicit
approximate analytical expression which compares well with numerical data. At
higher forcing space-time chaotic patterns are observed.Comment: submitted to Phys.Rev.
On small energy stabilization in the NLKG with a trapping potential
We consider a nonlinear Klein Gordon equation (NLKG) with short range
potential with eigenvalues and show that in the contest of complex valued
solutions the small standing waves are attractors for small solutions of the
NLKG. This extends the results already known for the nonlinear Schr\"odinger
equation and for the nonlinear Dirac equation. In addition, this extends a
result of Bambusi and Cuccagna (which in turn was an extension of a result by
Soffer and Weinstein) which considered only real valued solutions of the NLKG
Scattering in the energy space for Boussinesq equations
In this note we show that all small solutions in the energy space of the
generalized 1D Boussinesq equation must decay to zero as time tends to
infinity, strongly on slightly proper subsets of the space-time light cone. Our
result does not require any assumption on the power of the nonlinearity,
working even for the supercritical range of scattering. No parity assumption on
the initial data is needed
- …