Based on the generalized nonlinear Schrödinger equation model with sign-reversal varying-in-time harmonic oscillator
potential, we show that conditions of its exact integrability in one-dimensional case (1D) indicate conclusively the way
for solitonlike bullets generation in 3D nonautonomous nonlinear and dispersive systems. It turns out that generation of
matter-wave soliton bullets can be realized if periodic variations of nonlinearity and confining potential are opposite in
phases so that peaks of nonlinearity inside the atomic cloud coincide in time with repulsive character of trapping
potential. In nonlinear optical applications, periodic graded-index nonlinear structures with alternating wave-guiding and
anti-wave-guiding segments open remarkable opportunities in studies of BEC systems by performing experiments in
nonlinear optical systems.
Recent studies have thrown doubt on the ideal treatment of soliton tunneling. The most important enigmas in this
field can be formulated in the following way: As to whether nonlinear soliton tunneling effect will resemble more
the point like classical particle case or the quantum mechanical behavior in which the particle itself has an internal
structure? How "hidden" degrees of freedom can show up in the process of soliton tunneling? What happens if the
amplitude and duration of the input soliton vary in time when the soliton approaches a classically forbidden
barrier? In particular, what happens in the case of the nonlinear tunneling of self-compressing soliton when its
binding energy is increased? As to whether this case will resemble more the classical particle case or the quantum
mechanical behavior? These questions are taken up in this Report.
The discovery of stimulated Raman self-scattering (SRSS) effect of femtosecond optical solitons is acknowledged
to be among the most notable achievements of nonlinear fiber optics. This effect is also often called intrapulse
stimulated Raman scattering (ISRS), or soliton self-frequency shift (SSFS), thereby emphasizing the unusual
regime of stimulated Raman scattering, when the spectrum of a high-power ultrashort laser pulse proves to be so
broad that it covers the band of Raman resonances of the medium. The soliton-like wave packets with continuously
shifted spectrum traveling not only in the ordinary space and time, but also in the spectral space, are known as
colored femtosecond solitons. Colored solitons play an important role in the soliton supercontinuum generation.
The most interesting features of colored optical solitons are connected with the possibility of their tunneling in the
spectral domain through a potential barrier-like spectral inhomogeneity of group velocity dispersion (GVD),
including the forbidden band of positive GVD. This effect is known as soliton spectral tunneling effect (SST).
In this Report, we consider the influence of the soliton binding energy on dynamics of the SST effect assuming that
the amplitude and duration of the tunneling soliton vary in time when the soliton spectrum approaches a forbidden
GVD barrier. We show that soliton self-compressing effect has dramatic impact on the SST through forbidden
spectral region of positive GVD.
The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schrodinger equation model with
time-dependent confining harmonic oscillator potential. The model allows one to analyse on the general basis a variety
of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics and in nonlinear optics
and biophysics. The nonlinear effect of the soliton parametric resonance is investigated by using two complementary
methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible
denaturation of soliton bound states are also considered.
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