The higher grading structure of the WKI hierarchy and the two-component short pulse equation

A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Sch\" afer-Wayne short pulse equation arises quite naturally from the first negative flow of the WKI hierarchy. Some novel integrable nonautonomous models are also proposed. The conserved charges, both local and nonlocal, are obtained from the Riccati form of the spectral problem. The loop-soliton solutions of the WKI hierarchy are systematically constructed through gauge followed by reciprocal B\" acklund transformation, establishing the precise connection between the whole WKI and AKNS hierarchies. The connection between the short pulse equation with the sine-Gordon model is extended to a correspondence between the two-component short pulse equation and the Lund-Regge model

The algebraic structure behind the derivative nonlinear Schroedinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\" odinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of a $\hat{s\ell}_2$ Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows, respectively. The equivalence between the latter and the massive Thirring model is explicitly demonstrated also. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation.Comment: references adde

Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays

As photons do not interact with each other, it is interesting to ask whether photonic systems can be modified to exhibit the phases characteristic of strongly coupled many-body systems. We demonstrate how a Mott insulator type of phase of excitations can arise in an array of coupled electromagnetic cavities, each of which is coupled resonantly to a {\em single} two level system (atom/quantum dot/Cooper pair) and can be individually addressed from outside. In the Mott phase each atom-cavity system has the same integral number of net polaritonic (atomic plus photonic) excitations with photon blockade providing the required repulsion between the excitations in each site. Detuning the atomic and photonic frequencies suppresses this effect and induces a transition to a photonic superfluid. We also show that for zero detuning, the system can simulate the dynamics of many body spin systems.Comment: 4 pages, 3 figure

Genetic and combining ability analysis of some agronomic and grain quality characters in sorghum

The objective of this study was to evaluate the combining ability, heterosis and variance components of a set of selected restorers and male sterile in sorghum for the following characters: days to 50% flowering, plant height, panicle length, grain yeid for panicle, number of grains per panicle, thousand grain weight, grain breaking strength, % floaters, % water absorption, flour particle size index, rolling quality of the dough and gel spreadin

Differences Between The Optical/Uv Spectra Of X-Ray Bright And X-Ray Faint QSOs

We contrast measurements of composite optical and ultraviolet (UV) spectra constructed from samples of QSOs defined by their soft X-ray brightness. X-ray bright (XB) composites show stronger emission lines in general, but particularly from the narrow line region. The difference in the [OIII]/Hbeta ratio is particularly striking, and even more so when blended FeII emission is properly subtracted. The correlation of this ratio with X-ray brightness were principal components of QSO spectral diversity found by Boroson & Green (1992). We find here that other, much weaker narrow optical forbidden lines ([OII] and NeV) are enhanced by factors of 2 to 3 in our XB composites, and that narrow line emission is also strongly enhanced in the XB UV composite. Broad permitted line fluxes are slightly larger for all XB spectra, but the narrow/broad line ratio stays similar or increases strongly with X-ray brightness for all strong permitted lines except Hbeta. Spectral differences between samples divided by their relative X-ray brightness (as measured by alpha_{ox}) exceed those seen between complementary samples divided by luminosity or radio loudness. We propose that the Baldwin effect may be a secondary correlation to the primary relationship between alpha_{ox} and emission line equivalent width. We conclude that either 1) equivalent width depends strongly on the SHAPE of the ionizing continuum, as crudely characterized here by alpha_{ox} or 2) both equivalent width and alpha_{ox} are related to some third parameter characterizing the QSO physics. One such possibility is intrinsic warm absorption; a soft X-ray absorber situated between the broad and narrow line regions can successfully account for many of the properties observed.Comment: 16 pages including 3 figures, AAS latex, plus 4 tables totaling 5 pages, to appear in ApJ Vol. 498, May 1, 199

Influência do tamanho da semente na qualidade fisiológica e na produtividade da cultura da soja.

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