Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation

The non-topological, stationary and propagating, soliton solutions of the classical continuous Heisenberg ferromagnet equation are investigated. A general, rigorous formulation of the Inverse Scattering Transform for this equation is presented, under less restrictive conditions than the Schwartz class hypotheses and naturally incorporating the non-topological character of the solutions. Such formulation is based on a new triangular representation for the Jost solutions, which in turn allows an immediate computation of the asymptotic behaviour of the scattering data for large values of the spectral parameter, consistently improving on the existing theory. A new, general, explicit multi-soliton solution formula, amenable to computer algebra, is obtained by means of the matrix triplet method, producing all the soliton solutions (including breather-like and multipoles), and allowing their classification and descriptio

Stability of polar decompositions

Certain continuity properties of the factors in generalized polar decompositions of real and complex matrices are studied. A complete characterization is given of those generalized polar decompositions that persist under small perturbations in the matrix and in the scalar product. Connections are made with quadratic matrix equations, and with stability properties of certain invariant subspaces

Methicillin-Susceptible ST398 Staphylococcus aureus Responsible for Bloodstream Infections: An Emerging Human-Adapted Subclone?

In the course of an annual 3-month bloodstream infections (BSI) survey conducted during a four-year period in 31 healthcare institutions located in three noncontiguous French regions, we report 18 ST398 Staphylococcus aureus BSI. ST398 BSI incidence showed a seven-fold increase during the study period (0.002 per 1,000 patient days in 2007 vs. 0.014 in 2010). ST398 BSI isolates differed from the pig-borne multiresistant clone: 17/18 BSI isolates were methicillin susceptible and none was of t011, t034 or t108 pig-borne spa-types. ST398 BSI isolates had homogenous resistance patterns (15/18 with only Eryr) and prophagic content (all harboured the hlb-converting Sau3int phage). The clustering of BSI and pig-borne isolates by spa-typing and MLVA, the occurrence of Sau3int phage in BSI isolates and the lack of this phage in pig-borne isolates suggest that the emergence of BSI isolates could have arisen from horizontal transfer, at least of the Sau3int phage, in genetically diverse MSSA ST398 isolates. The acquisition of the phage likely plays a role in the increasing ability of the lysogenic ST398 isolates to colonize human. The mode of acquisition of the non pig-borne ST398 isolates by our 18 patients remains unclear. ST398 BSI were diagnosed in patients lacking livestock exposure and were significantly associated with digestive portals of entry (3/18 [16.7%] for ST398 vs. 19/767 [2.5%] for non ST398 BSI; p = .012). This raises the question of possible foodborne human infections. We suggest the need for active surveillance to study and control the spread of this human-adapted subclone increasingly isolated in the hospital setting

A unified approach to Darboux transformations

We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution. We show how this result provides a unified approach to Darboux transformations associated with various systems of ordinary differential operators. We illustrate our theory by deriving the Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a discrete eigenvalue is added to the spectrum.Comment: final version that will appear in Inverse Problem

Exact solutions to the focusing nonlinear Schrodinger equation

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigonometric, and polynomial functions of the spatial and temporal coordinates.Comment: 60 pages, 18 figure