465 research outputs found
New reductions of integrable matrix PDEs: -invariant systems
We propose a new type of reduction for integrable systems of coupled matrix
PDEs; this reduction equates one matrix variable with the transposition of
another multiplied by an antisymmetric constant matrix. Via this reduction, we
obtain a new integrable system of coupled derivative mKdV equations and a new
integrable variant of the massive Thirring model, in addition to the already
known systems. We also discuss integrable semi-discretizations of the obtained
systems and present new soliton solutions to both continuous and semi-discrete
systems. As a by-product, a new integrable semi-discretization of the Manakov
model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the
elementary function solutions of (a vector/matrix generalization of) the
derivative NLS equation can be expressed as the partial -derivatives of
elementary functions. Explicit soliton solutions are given in the author's
talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida
Soliton dynamics in deformable nonlinear lattices
We describe wave propagation and soliton localization in photonic lattices
which are induced in a nonlinear medium by an optical interference pattern,
taking into account the inherent lattice deformations at the soliton location.
We obtain exact analytical solutions and identify the key factors defining
soliton mobility, including the effects of gap merging and lattice imbalance,
underlying the differences with discrete and gap solitons in conventional
photonic structures.Comment: 5 pages, 4 figure
Multipole expansions in four-dimensional hyperspherical harmonics
The technique of vector differentiation is applied to the problem of the
derivation of multipole expansions in four-dimensional space. Explicit
expressions for the multipole expansion of the function r^n C_j (\hr) with
\vvr=\vvr_1+\vvr_2 are given in terms of tensor products of two
hyperspherical harmonics depending on the unit vectors \hr_1 and \hr_2. The
multipole decomposition of the function (\vvr_1 \cdot \vvr_2)^n is also
derived. The proposed method can be easily generalised to the case of the space
with dimensionality larger than four. Several explicit expressions for the
four-dimensional Clebsch-Gordan coefficients with particular values of
parameters are presented in the closed form.Comment: 19 pages, no figure
Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions
The light-induced frequency shift due to the hyperpolarizability (i.e. terms
of second-order in intensity) is studied for a forbidden optical transition,
=0=0. A simple universal dependence on the field ellipticity is
obtained. This result allows minimization of the second-order light shift with
respect to the field polarization for optical lattices operating at a magic
wavelength (at which the first-order shift vanishes). We show the possibility
for the existence of a magic elliptical polarization, for which the
second-order frequency shift vanishes. The optimal polarization of the lattice
field can be either linear, circular or magic elliptical. The obtained results
could improve the accuracy of lattice-based atomic clocks.Comment: 4 pages, RevTeX4, 2 eps fig
Solitary waves in mixtures of Bose gases confined in annular traps
A two-component Bose-Einstein condensate that is confined in a
one-dimensional ring potential supports solitary-wave solutions, which we
evaluate analytically. The derived solutions are shown to be unique. The
corresponding dispersion relation that generalizes the case of a
single-component system shows interesting features.Comment: 4 pages, 1 figur
Hyper-elliptic Nambu flow associated with integrable maps
We study hyper-elliptic Nambu flows associated with some dimensional maps
and show that discrete integrable systems can be reproduced as flows of this
class.Comment: 13 page
Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap
An ultrastable optical clock based on neutral atoms trapped in an optical
lattice is proposed. Complete control over the light shift is achieved by
employing the transition of
atoms as a "clock transition". Calculations of ac multipole polarizabilities
and dipole hyperpolarizabilities for the clock transition indicate that the
contribution of the higher-order light shifts can be reduced to less than 1
mHz, allowing for a projected accuracy of better than .Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Let
Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves
In this paper, an exact unitary transformation is examined that allows for
the construction of solutions of coupled nonlinear Schr{\"o}dinger equations
with additional linear field coupling, from solutions of the problem where this
linear coupling is absent. The most general case where the transformation is
applicable is identified. We then focus on the most important special case,
namely the well-known Manakov system, which is known to be relevant for
applications in Bose-Einstein condensates consisting of different hyperfine
states of Rb. In essence, the transformation constitutes a distributed,
nonlinear as well as multi-component generalization of the Rabi oscillations
between two-level atomic systems. It is used here to derive a host of periodic
and quasi-periodic solutions including temporally oscillating domain walls and
spiral waves.Comment: 6 pages, 4 figures, Phys. Rev. A (in press
Weak-Light Ultraslow Vector Optical Solitons via Electromagnetically Induced Transparency
We propose a scheme to generate temporal vector optical solitons in a
lifetime broadened five-state atomic medium via electromagnetically induced
transparency. We show that this scheme, which is fundamentally different from
the passive one by using optical fibers, is capable of achieving
distortion-free vector optical solitons with ultraslow propagating velocity
under very weak drive conditions. We demonstrate both analytically and
numerically that it is easy to realize Manakov temporal vector solitons by
actively manipulating the dispersion and self- and cross-phase modulation
effects of the system.Comment: 4 pages, 4 figure
Squared Eigenfunctions for the Sasa-Satsuma Equation
Squared eigenfunctions are quadratic combinations of Jost functions and
adjoint Jost functions which satisfy the linearized equation of an integrable
equation. In this article, squared eigenfunctions are derived for the
Sasa-Satsuma equation whose spectral operator is a system, while
its linearized operator is a system. It is shown that these squared
eigenfunctions are sums of two terms, where each term is a product of a Jost
function and an adjoint Jost function. The procedure of this derivation
consists of two steps: first is to calculate the variations of the potentials
via variations of the scattering data by the Riemann-Hilbert method. The second
one is to calculate the variations of the scattering data via the variations of
the potentials through elementary calculations. While this procedure has been
used before on other integrable equations, it is shown here, for the first
time, that for a general integrable equation, the functions appearing in these
variation relations are precisely the squared eigenfunctions and adjoint
squared eigenfunctions satisfying respectively the linearized equation and the
adjoint linearized equation of the integrable system. This proof clarifies this
procedure and provides a unified explanation for previous results of squared
eigenfunctions on individual integrable equations. This procedure uses
primarily the spectral operator of the Lax pair. Thus two equations in the same
integrable hierarchy will share the same squared eigenfunctions (except for a
time-dependent factor). In the Appendix, the squared eigenfunctions are
presented for the Manakov equations whose spectral operator is closely related
to that of the Sasa-Satsuma equation.Comment: 18 page
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