87 research outputs found
The modified nonlinear Schroedinger equation: Facts and artefacts
It is argued that the integrable modified nonlinear Schroedinger equation
with the nonlinearity dispersion term is the true starting point to
analytically describe subpicosecond pulse dynamics in monomode fibers. Contrary
to the known assertions, solitons of this equation are free of self-steepining
and the breather formation is possible.Comment: LaTeX2e, 8 pages, 1 figure, to be published in Europ. Phys. J.
Non-Linear Evolution Equations with Non-Analytic Dispersion Relations in 2+1 Dimensions. Bilocal Approach
A method is proposed of obtaining (2+1)-dimensional non- linear equations
with non-analytic dispersion relations. Bilocal formalism is shown to make it
possible to represent these equations in a form close to that for their
counterparts in 1+1 dimensions.Comment: 13 pages, to be published in J. Phys.
Dynamics of subpicosecond dispersion-managed soliton in a fibre: A perturbative analysis
A model is studied which describes a propagation of a subpicosecond optical
pulse in dispersion-managed fibre links. In the limit of weak chromatic
dispersion management, the model equation is reduced to a perturbed modified
NLS equation having a nonlinearity dispersion term. By means of the
Riemann--Hilbert problem, a perturbation theory for the soliton of the modified
NLS equation is developed. It is shown in the adiabatic approximation that
there exists a unique possibility to suppress the perturbation-induced shift of
the soliton centre at the cost of proper matching of the soliton width and
nonlinearity dispersion parameter. In the next-order approximation, the
spectral density of the radiation power emitted by a soliton is calculated.Comment: 16 pages, 3 figures, to appear in J. Mod. Optic
Full-time dynamics of modulational instability in spinor Bose-Einstein condensates
We describe the full-time dynamics of modulational instability in F=1 spinor
Bose-Einstein condensates for the case of the integrable three-component model
associated with the matrix nonlinear Schroedinger equation. We obtain an exact
homoclinic solution of this model by employing the dressing method which we
generalize to the case of the higher-rank projectors. This homoclinic solution
describes the development of modulational instability beyond the linear regime,
and we show that the modulational instability demonstrates the reversal
property when the growth of the modulation amplitude is changed by its
exponential decay.Comment: 6 pages, 2 figures, text slightly extended, a reference adde
Nonlinear Schr\"odinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
In this paper, we construct a generalized Darboux transformation for
nonlinear Schr\"odinger equation. The associated -fold Darboux
transformation is given both in terms of a summation formula and in terms of
determinants. As applications, we obtain compact representations for the -th
order rogue wave solutions of the focusing nonlinear Schr\"odinger equation and
Hirota equation. In particular, the dynamics of the general third order rogue
wave is discussed and shown to exhibit interesting structure.Comment: 17 pages, 4 figures, replaced by revised versio
Spatial Solitons in Media with Delayed-Response Optical Nonlinearities
Near-soliton scanning light-beam propagation in media with both
delayed-response Kerr-type and thermal nonlinearities is analyzed. The
delayed-response part of the Kerr nonlinearity is shown to be competitive as
compared to the thermal nonlinearity, and relevant contributions to a
distortion of the soliton form and phase can be mutually compensated. This
quasi-soliton beam propagation regime keeps properties of the incli- ned
self-trapped channel.Comment: 7 pages, to be published in Europhys. Let
Relaxation-induced stabilisation of optical pulsed vortex beams in media with a composite cubic-quintic nonlinearity
The problem of the generation of stable (quasi-stable) 3+1D light bullets in nonlinear media is addressed.
We consider a medium with a two-component relaxing cubic nonlinearity, and non-relaxing quintic one. It is
shown that a special adjustment of the pulse duration and the parameters of the two-component relaxing
nonlinearity enables one not only to suppress distortions of the temporal pulse envelope and self-induced
frequency shift, but to suppress a destructive effect of the azimuthal instability of vortex pulsed beams as well
The Gordon-Haus effect for modified NLS solitons
Random jitter in the soliton arrival time (the Gordon-Haus effect) is
analyzed for solitons being solutions of the integrable modified nonlinear
Schroedinger equation. It is shown that the mean square fluctuation of the
soliton position depends on the soliton parameters which can be properly
adjusted to suppress the Gordon-Haus jitter.Comment: LaTeX, 7 pages, 3 figures, to be published in Europhys. Let
The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications
The inverse spectral transform for the Zakharov-Shabat equation on the
semi-line is reconsidered as a Hilbert problem. The boundary data induce an
essential singularity at large k to one of the basic solutions. Then solving
the inverse problem means solving a Hilbert problem with particular prescribed
behavior. It is demonstrated that the direct and inverse problems are solved in
a consistent way as soon as the spectral transform vanishes with 1/k at
infinity in the whole upper half plane (where it may possess single poles) and
is continuous and bounded on the real k-axis. The method is applied to
stimulated Raman scattering and sine-Gordon (light cone) for which it is
demonstrated that time evolution conserves the properties of the spectral
transform.Comment: LaTex file, 1 figure, submitted to J. Phys.
Modulational instability in nonlocal Kerr-type media with random parameters
Modulational instability of continuous waves in nonlocal focusing and
defocusing Kerr media with stochastically varying diffraction (dispersion) and
nonlinearity coefficients is studied both analytically and numerically. It is
shown that nonlocality with the sign-definite Fourier images of the medium
response functions suppresses considerably the growth rate peak and bandwidth
of instability caused by stochasticity. Contrary, nonlocality can enhance
modulational instability growth for a response function with negative-sign
bands.Comment: 6 pages, 12 figures, revTeX, to appear in Phys. Rev.
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