Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models

New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics behaviour are presented as an example. The special attention is paid for the singular case $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde

Search for the Optical Counterpart of the Vela Pulsar X-ray Nebula

Observations of the Vela pulsar region with the Chandra X-ray observatory have revealed the fine structure of its synchrotron pulsar-wind nebula (PWN), which showed an overall similarity with the Crab PWN. However, contrary to the Crab, no firm detection of the Vela PWN in optical has been reported yet. To search for the optical counterpart of the X-ray PWN, we analyzed deep optical observations performed with different telescopes. We compared the optical images with those obtained with the Chandra ACIS to search for extended emission patterns which could be identified as counterparts of the X-ray nebula elements. Although some features are seen in the optical images, we find no correlation with the X-ray structure. Thus, we conclude that the diffuse optical emission is more likely associated with filaments in the host Vela SNR. The derived upper limits on the optical flux from the PWN are compatibile, within the uncertainties, with the values expected on the basis of the extrapolations of the X-ray data.Comment: 19 pages, 6 figures. Accepted for publication in Ap

Variability of the Vela Pulsar-wind Nebula Observed with Chandra

The observations of the pulsar-wind nebula (PWN) around the Vela pulsar with the Advanced CCD Imaging Spectrometer aboard the Chandra X-ray Observatory, taken on 2000 April 30 and November 30, reveal its complex morphology reminiscent of that of the Crab PWN. Comparison of the two observations shows changes up to 30% in the surface brightness of the PWN features. Some of the PWN elements show appreciable shifts, up to a few arcseconds (about 10^{16} cm), and/or spectral changes. To elucidate the nature of the observed variations, further monitoring of the Vela PWN is needed.Comment: 7 pages (incl. 3 embedded PS figures), AASTEX, uses emulateapj5.sty. Submitted to ApJ Lett. For a high-resolution color PS image of Figure 3 (6.3 Mby), see http://www.astro.psu.edu/users/divas/velaneb_fig3.p

Multicolor Photometry of the Vela Pulsar

Multicolor photometry of the Vela pulsar (PSR B0833-45), updated by recent HST/WFPC2 observations obtained in the 555W, 675W and 814W filters, is presented. The available data provide the best characterization so far of the pulsar spectral shape, which is dominated by a flat power law continuum with spectral index \alpha = -0.2 +/- 0.2, consistent with the extrapolation in the optical domain of the power law component of the X-ray spectrum detected by Chandra. In addition, a marginally significant dip (~ 3 sigma) seems to be present at about 6500 AA. Spectroscopic observations with the VLT, now in progress, will undoubtly provide a much better assessment of the reality and characteristics of this feature.Comment: 4 pages, LaTex, 2 Postscript figures. Astronomy & Astrophysics, accepte

Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio

Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field

We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a created pair of the quasi-particles, corresponding to a diagonal form of the instantaneous Hamiltonian. The case of an adiabatic change of the metric of homogeneous isotropic space is analyzed. We show that the created pairs of quasi-particles in de Sitter space should be interpreted as pairs of virtual particles.Comment: 7 pages, 3 figure

Polarization of Thermal X-rays from Isolated Neutron Stars

Since the opacity of a magnetized plasma depends on polarization of radiation, the radiation emergent from atmospheres of neutron stars with strong magnetic fields is expected to be strongly polarized. The degree of linear polarization, typically ~10-30%, depends on photon energy, effective temperature and magnetic field. The spectrum of polarization is more sensitive to the magnetic field than the spectrum of intensity. Both the degree of polarization and the position angle vary with the neutron star rotation period so that the shape of polarization pulse profiles depends on the orientation of the rotational and magnetic axes. Moreover, as the polarization is substantially modified by the general relativistic effects, observations of polarization of X-ray radiation from isolated neutron stars provide a new method for evaluating the mass-to-radius ratio of these objects, which is particularly important for elucidating the properties of the superdense matter in the neutron star interiors.Comment: 7 figures, to be published in Ap