29 research outputs found
Vortex -- Kink Interaction and Capillary Waves in a Vector Superfluid
Interaction of a vortex in a circularly polarized superfluid component of a
2d complex vector field with the phase boundary between superfluid phases with
opposite signs of polarization leads to a resonant excitation of a
``capillary'' wave on the boundary. This leads to energy losses by the
vortex--image pair that has to cause its eventual annihilation.Comment: LaTeX 7 pages, no figure
Quantum temporal correlations and entanglement via adiabatic control of vector solitons
It is shown that optical pulses with a mean position accuracy beyond the
standard quantum limit can be produced by adiabatically expanding an optical
vector soliton followed by classical dispersion management. The proposed scheme
is also capable of entangling positions of optical pulses and can potentially
be used for general continuous-variable quantum information processing.Comment: 5 pages, 1 figure, v2: accepted by Physical Review Letters, v3: minor
editing and shortening, v4: included the submitted erratu
Modulational instability and nonlocality management in coupled NLS system
The modulational instability of two interacting waves in a nonlocal Kerr-type
medium is considered analytically and numerically. For a generic choice of wave
amplitudes, we give a complete description of stable/unstable regimes for zero
group-velocity mismatch. It is shown that nonlocality suppresses considerably
the growth rate and bandwidth of instability. For nonzero group-velocity
mismatch we perform a geometrical analysis of a nonlocality management which
can provide stability of waves otherwise unstable in a local medium.Comment: 15 pages, 12 figures, to be published in Physica Script
Statistics of a noise-driven Manakov soliton
We investigate the statistics of a vector Manakov soliton in the presence of
additive Gaussian white noise. The adiabatic perturbation theory for Manakov
soliton yields a stochastic Langevin system which we analyze via the
corresponding Fokker-Planck equation for the probability density function (PDF)
for the soliton parameters. We obtain marginal PDFs for the soliton frequency
and amplitude as well as soliton amplitude and polarization angle. We also
derive formulae for the variances of all soliton parameters and analyze their
dependence on the initial values of polarization angle and phase.Comment: Submitted to J.Phys.A: Mathematical and Genera
Weak Transversality and Partially Invariant Solutions
New exact solutions are obtained for several nonlinear physical equations,
namely the Navier-Stokes and Euler systems, an isentropic compressible fluid
system and a vector nonlinear Schroedinger equation. The solution methods make
use of the symmetry group of the system in situations when the standard Lie
method of symmetry reduction is not applicable.Comment: 23 pages, preprint CRM-284
Instability of two interacting, quasi-monochromatic waves in shallow water
We study the nonlinear interactions of waves with a doubled-peaked power
spectrum in shallow water. The starting point is the prototypical equation for
nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries
equation. Using a multiple-scale technique two defocusing coupled Nonlinear
Schr\"odinger equations are derived. We show analytically that plane wave
solutions of such a system can be unstable to small perturbations. This
surprising result suggests the existence of a new energy exchange mechanism
which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure
Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries
We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys.
JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves
in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models
with two phase symmetries. MI of three-wave parametric spatial solitons due to
group velocity dispersion (GVD) is investigated as a typical example of such
models. We reveal a new branch of neck instability, which dominates the usual
snake type MI found for normal GVD. The resultant nonlinear evolution is
thereby qualitatively different from cases with only a single phase symmetry.Comment: 4 pages with figure
Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations
We present a detailed analysis of the modulational instability (MI) of
ground-state bright solitary solutions of two incoherently coupled nonlinear
Schr\"odinger equations. Varying the relative strength of cross-phase and
self-phase effects we show existence and origin of four branches of MI of the
two-wave solitary solutions. We give a physical interpretation of our results
in terms of the group velocity dispersion (GVD) induced polarization dynamics
of spatial solitary waves. In particular, we show that in media with normal GVD
spatial symmetry breaking changes to polarization symmetry breaking when the
relative strength of the cross-phase modulation exceeds a certain threshold
value. The analytical and numerical stability analyses are fully supported by
an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199
Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations
A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is
studied. To show the complete integrability of the model with multiple
components, we extend the discrete version of the inverse scattering method for
the single-component discrete nonlinear Schr\"{o}dinger equation proposed by
Ablowitz and Ladik. By means of the extension, the initial-value problem of the
model is solved. Further, the integrals of motion and the soliton solutions are
constructed within the framework of the extension of the inverse scattering
method.Comment: 27 pages, LaTeX2e (IOP style
Gain through losses in nonlinear optics
Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organization, pattern formation and noise amplification across diverse disciplines, including physics, chemistry, engineering and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied. In the present review article, we summarize the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced modulation instability, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources and pulsed lasers