599 research outputs found
Hamiltonian formalism of the DNLS equation with nonvanished boundary value
Hamiltonian formalism of the DNLS equation with nonvanishing boundary value
is developed by the standard procedure.Comment: 11 page
Darboux transformation for two component derivative nonlinear Schr\"odinger equation
In this paper, we consider the two component derivative nonlinear
Schr\"{o}dinger equation and present a simple Darboux transformation for it. By
iterating this Darboux transformation, we construct a compact representation
for the soliton solutions.Comment: 12 pages, 2 figure
Two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions
An explicit two-soliton solution for the derivative nonlinear Schr\"odinger
equation with nonvanishing boundary conditions is derived, demonstrating
details of interactions between two bright solitons, two dark solitons, as well
as one bright soliton and one dark soliton. Shifts of soliton positions due to
collisions are analytically obtained, which are irrespective of the bright or
dark characters of the participating solitons.Comment: 11 pages, 4 figures. Phys. Lett. A 2006 (in press
Two-Pulse Propagation in Media with Quantum-Mixed Ground States
We examine fully coherent two-pulse propagation in a lambda-type medium,
under two-photon resonance conditions and including inhomogeneous broadening.
We examine both the effects of short pulse preparation and the effects of
medium preparation. We contrast cases in which the two pulses have matched
envelopes or not, and contrast cases in which ground state coherence is present
or not. We find that an extended interpretation of the Area Theorem for
single-pulse self-induced transparency (SIT) is able to unify two-pulse
propagation scenarios, including some aspects of electromagnetically-induced
transparency (EIT) and stimulated Raman scattering (SRS). We present numerical
solutions of both three-level and adiabatically reduced two-level density
matrix equations and Maxwell's equations, and show that many features of the
solutions are quickly interpreted with the aid of analytic solutions that we
also provide for restricted cases of pulse shapes and preparation of the
medium. In the limit of large one-photon detuning, we show that the two-level
equations commonly used are not reliable for pulse Areas in the 2 range,
which allows puzzling features of previous numerical work to be understood.Comment: 28 pages, 7 figures. Replaced with version accepted in PR
Conserved Quantities in Gravity via Noether Symmetry
This paper is devoted to investigate gravity using Noether symmetry
approach. For this purpose, we consider Friedmann Robertson-Walker (FRW)
universe and spherically symmetric spacetimes. The Noether symmetry generators
are evaluated for some specific choice of models in the presence of
gauge term. Further, we calculate the corresponding conserved quantities in
each case. Moreover, the importance and stability criteria of these models are
discussed.Comment: 14 pages, accepted for publication in Chin. Phys. Let
Completely integrable models of non-linear optics
The models of the non-linear optics in which solitons were appeared are
considered. These models are of paramount importance in studies of non-linear
wave phenomena. The classical examples of phenomena of this kind are the
self-focusing, self-induced transparency, and parametric interaction of three
waves. At the present time there are a number of the theories based on
completely integrable systems of equations, which are both generations of the
original known models and new ones. The modified Korteweg-de Vries equation,
the non- linear Schrodinger equation, the derivative non-linear Schrodinger
equation, Sine-Gordon equation, the reduced Maxwell-Bloch equation, Hirota
equation, the principal chiral field equations, and the equations of massive
Thirring model are gradually putting together a list of soliton equations,
which are usually to be found in non-linear optics theory.Comment: Latex, 17 pages, no figures, submitted to Pramana
Differentially rotating disks of dust: Arbitrary rotation law
In this paper, solutions to the Ernst equation are investigated that depend
on two real analytic functions defined on the interval [0,1]. These solutions
are introduced by a suitable limiting process of Backlund transformations
applied to seed solutions of the Weyl class. It turns out that this class of
solutions contains the general relativistic gravitational field of an arbitrary
differentially rotating disk of dust, for which a continuous transition to some
Newtonian disk exists. It will be shown how for given boundary conditions (i.
e. proper surface mass density or angular velocity of the disk) the
gravitational field can be approximated in terms of the above solutions.
Furthermore, particular examples will be discussed, including disks with a
realistic profile for the angular velocity and more exotic disks possessing two
spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and
Gravitation
From AKNS to derivative NLS hierarchies via deformations of associative products
Using deformations of associative products, derivative nonlinear Schrodinger
(DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can
also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed
method to obtain 'functional representations' can be applied. We actually
consider hierarchies with dependent variables in any (possibly noncommutative)
associative algebra, e.g., an algebra of matrices of functions. This also
covers the case of hierarchies of coupled DNLS equations.Comment: 22 pages, 2nd version: title changed and material organized in a
different way, 3rd version: introduction and first part of section 2
rewritten, taking account of previously overlooked references. To appear in
J. Physics A: Math. Ge
A direct method of solution for the Fokas-Lenells derivative nonlinear Schr\"odinger equation: I. Bright soliton solutions
We develop a direct method of solution for finding the bright -soliton
solution of the Fokas-Lenells derivative nonlinear Schr\"odinger equation. The
construction of the solution is performed by means of a purely algebraic
procedure using an elementary theory of determinants and does not rely on the
inverse scattering transform method. We present two different expressions of
the solution both of which are expressed as a ratio of determinants. We then
investigate the properties of the solutions and find several new features.
Specifically, we derive the formula for the phase shift caused by the
collisions of bright solitons.Comment: To appear in J. Phys. A: Math. Theor. 45(2012) Ma
Primary alkylphosphine–borane polymers: Synthesis, low glass transition temperature, and a predictive capability thereof
With a multitude of potential applications, poly(phosphine–borane)s are an interesting class of polymer comprising main-group elements within the inorganic polymer backbone. A new family of primary alkylphosphine–borane polymers was synthesized by a solvent-free rhodium-catalyzed dehydrocoupling reaction and characterized by conventional chemicophysical techniques. The thermal stability of the polymers is strongly affected by the size and shape of the alkyl side chain with longer substituents imparting greater stability. The polymers show substantial stability toward UV illumination and immersion in water; however, they undergo a loss of alkylphosphine units during thermal degradation. The polymers exhibit glass transition temperatures (Tg) as low as −70 °C. A group interaction model (GIM) framework was developed to allow the semiquantitative prediction of Tg values, and the properties of the materials in this study were used to validate the model
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