Possibilities of analysis of brightness distributions for components of eclipsing variables from data of space photometry

We carried out numerical experiments on the evaluation of the possibilities of obtaining the information about brightness distributions for the components of eclipsing variables from the data of high-precision photometry expected for planned satellites COROT and Kepler. We examined a simple model of the eclipsing binary with the spherical components on circular orbits and the linear law of the limb darkening. The solutions of light curves have been obtained as by fitting of the nonlinear model, into the number of parameters of which included the limb darkening coefficients, so also by the solution of the ill-posed inverse problem of restoration of brightness distributions across the disks of stars without rigid model constraints on the form of these functions. The obtained estimations show that if the observational accuracy amounts to 0.0001 then the limb darkening coefficients can be found with the relative error approximately 0.01 . The brightness distributions across the disks of components can be restored also nearly with the same accuracy.Comment: 12 pages LaTeX, 6 figures, Contributed paper at the All-Russian Astronomical conference "Close Binary Stars in Modern Astrophysics (MARTYNOV-2006)" held in Moscow, Russia May 22 - 24, 200

Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type

Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an associated complex curve (Sato function) and corresponding generating equations. Dispersionless KP and 2DTL hierarchy are considered as illustrative examples.Comment: 16 pages, LaTe

M\"obius invariant integrable lattice equations associated with KP and 2DTL hierarchies

Integrable lattice equations arising in the context of singular manifold equations for scalar, multicomponent KP hierarchies and 2D Toda lattice hierarchy are considered. These equation generate the corresponding continuous hierarchy of singular manifold equations, its B\"acklund transformations and different forms of superposition principles. They possess rather special form of compatibility representation. The distinctive feature of these equations is invariance under the action of M\"obius transformation. Geometric interpretation of these discrete equations is given.Comment: 13 pages, LaTeX; talk at SIDE III conference, Sabaudia, Italy, May 199

Generalized KP hierarchy: M\"obius Symmetry, Symmetry Constraints and Calogero-Moser System

Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius symmetry transformation for the singular manifold equation leads to continuous or discrete non-isospectral symmetry of the basic (scalar or multicomponent KP) hierarchy connected with binary B\"acklund transformation. A more general class of multicomponent M\"obius-type symmetries is studied. It is demonstrated that symmetry constraints of KP hierarchy defined using multicomponent M\"obius-type symmetries give rise to Calogero-Moser system.Comment: 18 pages, LaTeX, talk at "Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives" (August 1999, Chernogolovka, Russia

Restoration of Brightness Distributions across Quasar's Accretion Disk from Observations of High Magnification Events in Components of Gravitational Lens QSO 2237+0305

We present a technique for the successive restoration of the branches of the one-dimensional strip brightness distribution across a quasar's accretion disk via the analysis of observations of high magnification events in measured fluxes from the multiple quasar images produced by a gravitational lens. Hypothesizing these events to by associated with microlensing by a fold caustic, the branches of brightness distribution are searched for on compact sets of non-negative, monotonically non-increasing, convex downward functions. The results of numerical simulations show that the solution obtained is stable against random noise. Analysis of the light curves of high magnification events in the fluxes from components C and A of the gravitational lens QSO 2237+0305, observed by the OGLE and GLITP groups, has yielded the forms of the strip brightness distributions across the accretion disk of the lensed quasar. The resulting sizes of the accretion disk are in agreement with results obtained earlier via model-fitting. The form of the brightness distribution is consistent with the expected appearance of an accretion disk rotating around supermassive black hole.Comment: 12 pages, 6 figures, LaTex. Contributed paper at the conference VAK-2004 "Horizons of Universe" (Moscow, Russia, June 3 - 10, 2004

Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchy

Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. Resolution of these functional equations leads to the $\tau$-function and addition formulae to it. General discrete transformations of the $\tau$-function are presented in the determinant form. Closed one-form and other formulae also arise naturally within the approach proposed. Generalized KP hierarchy written in terms of different invariants of Combescure symmetry transformations coincides with the usual KP hierarchy and the mKP hierarchy.Comment: 25 pages, LaTe

Relation of Atmosphere Surface Pressure Fluctuations with Geomagnetic and Cosmic Factors

We present results of the digital spectral analysis of the time series containing the daily samples of the atmosphere surface pressure measured at Saratov city from Jan 1, 1995 to Dec 31, 1999. We calculated also cross correlation functions between the pressure fluctuations and the planetary geomagnetic indices, Ap and Cp, and cross correlation function between these fluctuations and the cosmic-ray intensity. Two peaks detected in the calculated power spectrum are related, probably, with the atmosphere tidal waves. The relation of the pressure fluctuations with the Ap index of the geomagnetic activity is statistically insignificant. The cross correlation function between the pressure fluctuations and the Cp index has the maximal value 0.044+-0.023 at the pressure time delay 4 days. The statistically significant negative correlation is discovered between the surface pressure fluctuations and the cosmic-ray intensity. The cross correlation function has two minima: at the zero time delay with the value -0.068+-0.023, and at the pressure time delay 12 days with the value -0.087+-0.023. The negative correlation between the pressure and the cosmic-ray intensity is observed at the pressure time delay as long as 17 days and can be explained by the so-called condensation mechanism of an interaction of the cosmic rays with the atmosphere.Comment: 5 pages, LaTeX. Presented at VI International Telecommunicational Conference "Youth and Science", Oct 10 - Dec 20, 2002, Moscow, Russi

Generalized integrable hierarchies and Combescure symmetry transformations

Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical meaning, are in fact the symmetry transformations of generalized integrable hierarchies. Generalized equation written in terms of invariants of Combescure transformations are the usual integrable equations and their modified partners. The KP-mKP, DS-mDS hierarchies and Darboux system are considered.Comment: 17 pages, LaTe

Integrability properties of symmetric 4+4-dimensional heavenly type equation

We demonstrate that the dispersionless $\bar\partial$-dressing method developed before for general heavenly equation is applicable to the $4+4$ and $2N+2N$ - dimensional symmetric heavenly type equations. We introduce generating relation and derive the two-form defining the potential and equation for it. We develop the dressing scheme, calculate a class of special solutions and demonstrate that reduction from $4+4$-dimensional equation to four-dimensional general heavenly equation can be effectively performed on the level of the dressing data. We consider also the extension of the proposed scheme to $2N+2N$-dimensional case.Comment: 14 page

On dispersionless BKP hierarchy and its reductions

Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the $\tau$-function and conformally invariant equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry constraints for the dBKP hierarchy are studied.Comment: 11 page