Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

An Imaging and Spectral Study of Ten X-Ray Filaments around the Galactic Center

We report the detection of 10 new X-ray filaments using the data from the {\sl Chandra} X-ray satellite for the inner $6^{\prime}$ ($\sim 15$ parsec) around the Galactic center (GC). All these X-ray filaments are characterized by non-thermal energy spectra, and most of them have point-like features at their heads that point inward. Fitted with the simple absorbed power-law model, the measured X-ray flux from an individual filament in the 2-10 keV band is $\sim 2.8\times10^{-14}$ to $10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ and the absorption-corrected X-ray luminosity is $\sim 10^{32}-10^{33}$ ergs s$^{-1}$ at a presumed distance of 8 kpc to the GC. We speculate the origin(s) of these filaments by morphologies and by comparing their X-ray images with the corresponding radio and infrared images. On the basis of combined information available, we suspect that these X-ray filaments might be pulsar wind nebulae (PWNe) associated with pulsars of age $10^3 \sim 3\times 10^5$ yr. The fact that most of the filament tails point outward may further suggest a high velocity wind blowing away form the GC.Comment: 29 pages with 7 figures and 3 pages included. Accepted to Ap