Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves

The use of RAPD markers to detect genetic patterns in Aleurodicus dispersus (Hemiptera : Aleyrodidae) populations from the Canary Islands

Aleurodicus dispersus Russell (Hemiptera: Aleyrodidae), a highly polyphagous species, has since the 90’s been an important pest of ornamentals and tropical crops in the Canary Islands. In this study the RAPD-PCR technique was used to study the genetic structure of this whitefly in this archipelago. A total of 68 different bands were scored in seven populations using six primers for amplification. No differences in RAPD patterns were found among populations from different islands of the Canaries. These findings indicate a very high genetic similarity among populations and low level of genetic variability and support a single colonization event by few A. dispersus whiteflies and recent dispersion throughout the archipelago

Idoneidad de especies vegetales para el desarrollo poblacional de Neophilaenus campestris (Fallén) (Hemiptera: Aphrophoridae)

El conocimiento de la biología y dinámica poblacional de los insectos vectores de la bacteria fitopatógena Xylella fastidiosa Wells et al., 1987, es fundamental para llevar a cabo un adecuado control de las enfermedades que produce en plantas cultivadas, por medio del manejo de dichos vectores. En la Comunidad Valenciana, en la Zona Demarcada por presencia de la bacteria localizada en la provincia de Alicante, Philaenus spumarius (Linnaeus, 1758), Neophilaenus campestris (Fallén, 1805) y Neophilaenus lineatus (Linnaeus, 1758) han evidenciado portar la bacteria, si bien solo las dos primeras especies son vectores reconocidos en Europa

Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials

In this paper, we study the competition of linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtained detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions.Comment: 13 pages, 4 figure

Collapse in boson-fermion mixtures with all-repulsive interactions

We describe the collapse of the bosonic component in a boson-fermion mixture due to the pressure exerted on them by a large fermionic component, leading to collapse in a system with all-repulsive interactions. We describe the phenomena early collapse and of super-slow collapse of the mixture.Comment: 5 page

Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger equations with inhomogeneous parameters, including a linear coupling. For that system we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnoselskii fixed point theorem together with a suitable compactness criterion.Comment: 16 page

Gas phase Elemental abundances in Molecular cloudS (GEMS) VII. Sulfur elemental abundance

Gas phase Elemental abundances in molecular CloudS (GEMS) is an IRAM 30m large program aimed at determining the elemental abundances of carbon (C), oxygen (O), nitrogen (N), and sulfur (S) in a selected set of prototypical star-forming filaments. In particular, the elemental abundance of S remains uncertain by several orders of magnitude and its determination is one of the most challenging goals of this program. We have carried out an extensive chemical modeling of the fractional abundances of CO, HCO$^+$, HCN, HNC, CS, SO, H$_2$S, OCS, and HCS$^+$ to determine the sulfur depletion toward the 244 positions in the GEMS database. These positions sample visual extinctions from A$_V$ $\sim$ 3 mag to $>$50 mag, molecular hydrogen densities ranging from a few 10$^3$~cm$^{-3}$ to 3$\times$10$^6$~cm$^{-3}$, and T$_k$ $\sim$ 10$-$35 K. Most of the positions in Taurus and Perseus are best fitted assuming early-time chemistry, t=0.1 Myr, $\zeta_{H_2}$$\sim$ (0.5$-$1)$\times$10$^{-16}$ s$^{-1}$, and [S/H]$\sim$1.5$\times$10$^{-6}$. On the contrary, most of the positions in Orion are fitted with t=1~Myr and $\zeta_{H_2}$$\sim$ 10$^{-17}$ s$^{-1}$. Moreover, $\sim$40% of the positions in Orion are best fitted assuming the undepleted sulfur abundance, [S/H]$\sim$1.5$\times$10$^{-5}$. Our results suggest that sulfur depletion depends on the environment. While the abundances of sulfur-bearing species are consistent with undepleted sulfur in Orion, a depletion factor of $\sim$20 is required to explain those observed in Taurus and Perseus. We propose that differences in the grain charge distribution in the envelopes of the studied clouds might explain these variations. The shocks associated with past and ongoing star formation could also contribute to enhance [S/H] in Orion.Comment: 22 pages, 15 figures, Astronomy and Astrophysics, in pres