415 research outputs found
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
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
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
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
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
INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING
Zakharov-Shabat--Ablowitz-Kaup-Newel-Segur representation for
Stokes-anti-Stokes stimulated Raman scattering is proposed. Periodical waves,
solitons and self-similarity solutions are derived. Transient and bright
threshold solitons are discussed.Comment: 16 pages, LaTeX, no figure
The Darboux transformation of the derivative nonlinear Schr\"odinger equation
The n-fold Darboux transformation (DT) is a 2\times2 matrix for the
Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed
by a ratio of determinant and determinant of
eigenfunctions. Using these formulae, the expressions of the and
in KN system are generated by n-fold DT. Further, under the reduction
condition, the rogue wave,rational traveling solution, dark soliton, bright
soliton, breather solution, periodic solution of the derivative nonlinear
Schr\"odinger(DNLS) equation are given explicitly by different seed solutions.
In particular, the rogue wave and rational traveling solution are two kinds of
new solutions. The complete classification of these solutions generated by
one-fold DT is given in the table on page.Comment: 21 papge, 10 figure
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