Towards an Inverse Scattering theory for non decaying potentials of the heat equation

The resolvent approach is applied to the spectral analysis of the heat equation with non decaying potentials. The special case of potentials with spectral data obtained by a rational similarity transformation of the spectral data of a generic decaying potential is considered. It is shown that these potentials describe $N$ solitons superimposed by Backlund transformations to a generic background. Dressing operators and Jost solutions are constructed by solving a DBAR-problem explicitly in terms of the corresponding objects associated to the original potential. Regularity conditions of the potential in the cases N=1 and N=2 are investigated in details. The singularities of the resolvent for the case N=1 are studied, opening the way to a correct definition of the spectral data for a generically perturbed soliton.Comment: 22 pages, submitted to Inverse Problem

Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets

A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed whithin the anyon theory. Thus, we show that static magnetic vortices correspond to the self-dual Chern - Simons solitons and are described by the Liouville equation. The related magnetic topological charge is associated with the electric charge of anyons. Furthermore, vortex - antivortex configurations are described by the sinh-Gordon equation and its conformally invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199

Phthiraptera and Gamasida Parasites of Columbina picui (Temminck) (Columbiformes: Columbidae) in the State of Rio Grande do Sul, Southern Brazil

Thirty-two specimens of Columbina picui (picui ground-dove) were examined, and a collection of arthropods was made by washing the external surface of the body and the nasal cavity. The species in the order Phthiraptera found and their respective prevalences, mean abundance and mean intensity were: Columbicola passerinae (84.4%; 10.3; 12.2), Hohorstiella passerinae (21.9%; 0.7; 3.1) and Physconelloides eurysema (3.1%; 0.1; 2). The gamasid mites found in the birds and their respective prevalences, mean abundance and mean intensity were: Pellonyssus marui (31.3%; 1.2; 3.9), Ornithonyssus bursa (15.6%; 0.2. ;1.2) and Mesonyssus sp. (6.3%; 0.1; 1). Columbicola passerinae, H. passerinae, P. eurysema, O. bursa, P. marui and Mesonyssus sp. were recorded for the first time infecting C. picui in Brazil. Except for O. bursa, the other species are reported for the first time in the state of Rio Grande do Sul, Brazil