Darboux transformation and multi-soliton solutions of Two-Boson hierarchy

We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on $SL(2,R)$ within the AKNS framework, this model is based on $SL(2,R)\otimes U(1)$. The connection between the scalar and the matrix descriptions in this case implies that the generic Darboux matrix for the TB hierarchy has a different structure from that in the models based on $SL(2,R)$ studied thus far. The conventional Darboux transformation is shown to be quite restricted in this model. We construct a modified Darboux transformation which has a much richer structure and which also allows for multi-soliton solutions to be written in terms of Wronskians. Using the modified Darboux transformations, we explicitly construct one soliton/kink solutions for the model.Comment:

Structure in the nucleus of NGC 1068 at 10 microns

New 8 to 13 micron array camera images of the central kiloparsec of Seyfert 2 galaxy NGC 1068 resolve structure that is similar to that observed at visible and radio wavelengths. The images reveal an infrared source which is extended and asymmetric, with its long axis oriented at P.A. 33 deg. Maps of the spatial distribution of 8 to 13 micron color temperature and warm dust opacity are derived from the multiwavelength infrared images. The results suggest that there exist two pointlike luminosity sources in the central regions of NGC 1068, with the brighter source at the nucleus and the fainter one some 100 pc to the northeast. This geometry strengthens the possibility that the 10 micron emission observed from grains in the nucleus is powered by a nonthermal source. In the context of earlier visible and radio studies, these results considerably strengthen the case for jet induced star formation in NGC 1068

Gamma-Ray Bursts as a Probe of the Very High Redshift Universe

We show that, if many GRBs are indeed produced by the collapse of massive stars, GRBs and their afterglows provide a powerful probe of the very high redshift (z > 5) universe.Comment: To appear in Proc. of the 5th Huntsville Gamma-Ray Burst Symposium, 5 pages, LaTe

The 8.3 and 12.4 micron imaging of the Galactic Center source complex with the Goddard infrared array camera

A 30 x 30 arcsec field at the Galactic Center (1.5 x 1.5 parsec) was mapped at 8.3 microns and 12.41 microns with high spatial resolution and accurate relative astrometry, using the 16 x 16 Si:Bi accumulation mode charge injection device Goddard infrared array camera. The design and performance of the array camera detector electronics system and image data processing techniques are discussed. Color temperature and dust opacity distributions derived from the spatially accurate images indicate that the compact infrared sources and the large scale ridge structure are bounded by warmer, more diffuse material. None of the objects appear to be heated appreciably by internal luminosity sources. These results are consistent with the model proposing that the complex is heated externally by a strong luminosity source at the Galactic Center, which dominates the energetics of the inner few parsecs of the galaxy

Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

Previously Claimed(/Unclaimed) X-ray Emission Lines in High Resolution Afterglow Spectra

We review the significance determination for emission lines in the Chandra HETGS spectrum for GRB020813, and we report on a search for additional lines in high resolution Chandra spectra. No previously unclaimed features are found. We also discuss the significance of lines sets reportedly discovered using XMM data for GRB011211 and GRB030227. We find that these features are likely of modest, though not negligible, significance.Comment: 4 pages, 1 figures, to appear in Santa Fe GRB Conference Proceedings, 200

Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 + y^2, multiplied by an analytic function P(z) of the single complex variable z= x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur

Chandra Observations of the Optically Dark GRB030528

The X-ray-rich GRB030528 was detected by the HETE satellite and its localization was rapidly disseminated. However, early optical observations failed to detect a counterpart source. In a 2-epoch ToO observation with Chandra, we discovered a fading X-ray source likely counterpart to GRB030528. The source brightness was typical of X-ray afterglows observed at similar epochs. Other observers detected an IR source at a location consistent with the X-ray source. The X-ray spectrum is not consistent with a large absorbing column.Comment: 4 pages, 1 figures, to appear in Santa Fe GRB Conference Proceedings, 200

Massive particles in acoustic space-times emergent inertia and passive gravity

I show that massive-particle dynamics can be simulated by a weak, spherical, external perturbation on a potential flow in an ideal fluid. The effective Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the particle relative to the fluid and c the speed of sound. This can serve as a model for emergent relativistic inertia a la Mach's principle with m playing the role of inertial mass, and also of analog gravity where it is also the passive gravitational mass. m depends on the particle type and intrinsic structure, while L is universal: For D dimensional particles L is proportional to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same way in the analog gravitational field independent of their internal structure, thus satisfying the weak equivalence principle. For D less or equal 5 they all have a relativistic limit with the acquired energy and momentum diverging as U approaches c. For D less or equal 7 the null geodesics of the standard acoustic metric solve our equation of motion. Interestingly, for D=4 the dynamics is very nearly Lorentzian. The particles can be said to follow the geodesics of a generalized acoustic metric of a Finslerian type that shares the null geodesics with the standard acoustic metric. In vortex geometries, the ergosphere is automatically the static limit. As in the real world, in ``black hole'' geometries circular orbits do not exist below a certain radius that occurs outside the horizon. There is a natural definition of antiparticles; and I describe a mock particle vacuum in whose context one can discuss, e.g., particle Hawking radiation near event horizons.Comment: 15 page: version published in Physical Review