3,562 research outputs found
Solutions for real dispersionless Veselov-Novikov hierarchy
We investigate the dispersionless Veselov-Novikov (dVN) equation based on the
framework of dispersionless two-component BKP hierarchy. Symmetry constraints
for real dVN system are considered. It is shown that under symmetry reductions,
the conserved densities are therefore related to the associated Faber
polynomials and can be solved recursively. Moreover, the method of hodograph
transformation as well as the expressions of Faber polynomials are used to find
exact real solutions of the dVN hierarchy.Comment: 14 page
Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
Dunajski generalization of the second heavenly equation is studied. A
dressing scheme applicable to Dunajski equation is developed, an example of
constructing solutions in terms of implicit functions is considered. Dunajski
equation hierarchy is described, its Lax-Sato form is presented. Dunajsky
equation hierarchy is characterized by conservation of three-dimensional volume
form, in which a spectral variable is taken into account.Comment: 13 page
Lattice and q-difference Darboux-Zakharov-Manakov systems via -dressing method
A general scheme is proposed for introduction of lattice and q-difference
variables to integrable hierarchies in frame of -dressing
method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov
systems of equations are derived. Darboux, B\"acklund and Combescure
transformations and exact solutions for these systems are studied.Comment: 8 pages, LaTeX, to be published in J Phys A, Letters
The properties of isolated chiral skyrmions in thin magnetic films
Axisymmetric solitonic states (chiral skyrmions) have been predicted
theoretically more than two decades ago. However, until recently they have been
observed in a form of skyrmionic condensates (hexagonal lattices and other
mesophases). In this paper we report experimental and theoretical
investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers
two years ago (Science 341 , 636 (2013)). The results of spin-polarized
scanning tunneling microscopy analyzed within the continuum and discrete models
provide a consistent description of isolated skyrmions in thin layers. The
existence region of chiral skyrmions is restricted by strip-out instabilities
at low fields and a collapse at high fields. We demonstrate that the same
equations describe axisymmetric localized states in all condensed matter
systems with broken mirror symmetry, and thus our findings establish basic
properties of isolated skyrmions common for chiral liquid crystals, different
classes of noncentrosymmetric magnets, ferroelectrics, and multiferroics.Comment: 12 pages, 12 figure
Neutral skyrmion configurations in the low-energy effective theory of spinor condensate ferromagnets
We study the low-energy effective theory of spinor condensate ferromagnets
for the superfluid velocity and magnetization degrees of freedom. This
effective theory describes the competition between spin stiffness and a
long-ranged interaction between skyrmions, topological objects familiar from
the theory of ordinary ferromagnets. We find exact solutions to the non-linear
equations of motion describing neutral configurations of skyrmions and
anti-skyrmions. These analytical solutions provide a simple physical picture
for the origin of crystalline magnetic order in spinor condensate ferromagnets
with dipolar interactions. We also point out the connections to effective
theories for quantum Hall ferromagnets.Comment: 13 pages, 7 figure
Probing Red Giant Atmospheres with Gravitational Microlensing
Gravitational microlensing provides a new technique for studying the surfaces
of distant stars. Microlensing events are detected in real time and can be
followed up with precision photometry and spectroscopy. This method is
particularly adequate for studying red giants in the Galactic bulge. Recently
we developed an efficient method capable of computing the lensing effect for
thousands of frequencies in a high-resolution stellar spectrum. Here we
demonstrate the effects of microlensing on synthesized optical spectra of red
giant model atmospheres. We show that different properties of the stellar
surface can be recovered from time-dependent photometry and spectroscopy of a
point-mass microlensing event with a small impact parameter. In this study we
concentrate on center-to-limb variation of spectral features. Measuring such
variations can reveal the depth structure of the atmosphere of the source star.Comment: 23 pages with 11 Postscript figures, submitted to ApJ; Section 2
expanded, references added, text revise
Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets
A phenomenological theory of magnetic states in noncentrosymmetric tetragonal
antiferromagnets is developed, which has to include homogeneous and
inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya
couplings. Magnetic properties of this class of antiferromagnets with low
crystal symmetry are discussed in relation to its first known members, the
recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry
and magnetic ordering in these systems allow the simultaneous occurrence of
chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of
incommensurate magnetic structures are possible, namely, chiral helices with
rotation of staggered magnetization and oscillations of the total
magnetization. Field-induced reorientation transitions into modulated states
have been studied and corresponding phase diagrams are constructed. Structures
of magnetic defects (domain-walls and vortices) are discussed. In particular,
vortices, i.e. localized non-singular line defects, are stabilized by the
inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric
antiferromagnets.Comment: 18 pages RevTeX4, 13 figure
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.
Intermediate phase in the spiral antiferromagnet Ba_2CuGe_2O_7
The magnetic compound Ba_2CuGe_2O_7 has recently been shown to be an
essentially two-dimensional spiral antiferromagnet that exhibits an
incommensurate-to-commensurate phase transition when a magnetic field applied
along the c-axis exceeds a certain critical value H_c. The T=0 dynamics is
described here in terms of a continuum field theory in the form of a nonlinear
sigma model. We are thus in a position to carry out a complete calculation of
the low-energy magnon spectrum for any strength of the applied field throughout
the phase transition. In particular, our spin-wave analysis reveals
field-induced instabilities at two distinct critical fields H_1 and H_2 such
that H_1 < H_c < H_2. Hence we predict the existence of an intermediate phase
whose detailed nature is also studied to some extent in the present paper.Comment: 15 pages, 11 figures, 2 table
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