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In this paper, a nonlocal two-component complex modified Korteweg–de Vries (mKdV) equation is investigated and its Darboux transformation is derived. By using the Darboux transformation, soliton solutions are obtained which include dark soliton solution, quasi-W-type soliton, quasi-M-type soliton and periodic solution.

A partir des donnees issues du recensement general de la population de 2014, nous analysons a l’echelle des bassins de vie, le lien entre migration residentielle a destination des espaces ruraux et periurbains et segregation socio-spatiale. Nos resultats montrent que les individus sont sensibles aux caracteristiques sociodemographiques du voisinage dans leurs territoires d’origine et de destination. Alors que le capital humain est source de retention pour les territoires d’origine, les individus mobiles apparaissent sensibles au degre d’homogeneite sociale des territoires. Enfin, l’influence des caracteristiques sociodemographiques sur les migrations residentielles vers les territoires ruraux et periurbains varie selon les categories socioprofessionnelles.Classification JEL : J61, R23, R15, C01.

Although straw mulching and nitrogen applications are extensively practiced in the agriculture sector, large uncertainties remain about their impacts on crop yields and especially the environment. The responses of summer maize yields, fertilizer use efficiency, and greenhouse gas (GHG) emissions including carbon dioxide (CO

It is a challenge to characterize soil respiration of crop residue return systems in the North China Plain (NCP) under no-tillage (NT) and conventional tillage (CT) practices. In this study, we addressed the "hot spot" research challenge of impacts of tillage practices on soil carbon storage and soil CO

Background: Japanese quail (Coturnix japonica) are important and widely distributed poultry in China. Researchers continue to pursue genetic selection for heavier quail. The intestinal microbiota plays a substantial role in growth promotion; however, the mechanisms involved in growth promotion remain unclear.Results: We generated 107.3 Gb of cecal microbiome data from ten Japanese quail, providing a series of quail gut microbial gene catalogs (1.25 million genes). We identified a total of 606 main microbial species from 1,033,311 annotated genes distributed among the ten quail. Seventeen microbial species from the genera Anaerobiospirillum, Alistipes, Barnesiella, and Butyricimonas differed significantly in their abundances between the female and male gut microbiotas. Most of the functional gut microbial genes were involved in metabolism, primarily in carbohydrate transport and metabolism, as well as some active carbohydrate-degrading enzymes. We also identified 308 antibiotic-resistance genes (ARGs) from the phyla Bacteroidetes, Firmicutes and Euryarchaeota. Studies of the differential gene functions between sexes indicated that abundances of the gut microbes that produce carbohydrate-active enzymes varied between female and male quail. Bacteroidetes was the predominant ARG-containing phylum in female quail; Euryarchaeota was the predominant ARG-containing phylum in male quail.Conclusion: This article provides the first description of the gene catalog of the cecal bacteria in Japanese quail as well as insights into the bacterial taxa and predictive metagenomic functions between male and female quail to provide a better understanding of the microbial genes in the quail ceca.

Agricultural tillage practices have a significant impact on the generation and consumption of greenhouse gases (GHGs), the primary causes of global warming. Two tillage systems, conventional tillage (CT) and no-tillage (NT), were compared to evaluate their effects on GHG emissions in this study. Averaged from 2018 to 2020, significant decreases of CO

In this paper, we investigate a multi-component AB system that appears in geophysical fluid dynamics. We construct bright–dark soliton solutions of the system using the Hirota’s bilinear method. We obtain asymptotic behaviors of two-soliton solution for the two-component AB system and prove that the interactions between two bright and two dark solitons are elastic. Under various parameter conditions, the oblique interactions and bound states of solitons are analyzed in detail. By use of the Pfaffian technique, we present N -bright and N − dark soliton solutions of the two- and multi-component AB system. The results obtained in this paper can be helpful for the study of vector multi-dark solitons in many physical systems such as nonlinear optics and fluid dynamics.

River ecosystems are under increasing stress in the background of global change and ever-growing anthropogenic impacts in Central Asia. However, available water quality data in this region are insufficient for a reliable assessment of the current status, which come as no surprise that the limited knowledge of regulating processes for further prediction of solute variations hinders the development of sustainable management strategies. Here, we analyzed a dataset of various water quality variables from two sampling campaigns in 2019 in the catchments of two major rivers in Central Asia—the Amu Darya and Syr Darya Rivers. Our results suggested high spatial heterogeneity of salinity and major ion components along the longitudinal directions in both river catchments, pointing to an increasing influence of human activities toward downstream areas. We linked the modeling outputs from the global nutrient model (IMAGE-GNM) to riverine nutrients to elucidate the effect of different natural and anthropogenic sources in dictating the longitudinal variations of the riverine nutrient concentrations (N and P). Diffuse nutrient loadings dominated the export flux into the rivers, whereas leaching and surface runoff constituted the major fractions for N and P, respectively. Discharge of agricultural irrigation water into the rivers was the major cause of the increases in nutrients and salinity. Given that the conditions in Central Asia are highly susceptible to climate change, our findings call for more efforts to establish holistic management of water quality.

In this paper, we study a nonintegrable discrete nonlinear Schrdinger (dNLS) equation with nonlinear hopping. By using the planar nonlinear dynamical map approach, we address the spatial properties of the nonintegrable dNLS equation. Through the constructions of exact period-1 and period-2 orbits of a planar nonlinear map which is a stationary version of the nonintegrable dNLS equation, we obtain the spatially periodic solutions of the nonintegrable dNLS equation. We also give the numerical simulations of the orbits of the planar nonlinear map and show how the nonlinear hopping terms affect those orbits. By using discrete Fourier transformation method, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation.

To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu–Eckhaus equation is derived from the reduction in an extended Ablowitz–Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu–Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.

In this paper, we investigate a general integrable nonlocal coupled nonlinear Schrodinger (NLS) system with the parity-time (PT) symmetry, which contains not only the nonlocal self-phase modulation and the nonlocal cross-phase modulation, but also the nonlocal four-wave mixing terms. This nonlocal coupled NLS system is a nonlocal version of a coupled NLS system. The general N-th Darboux transformation for the nonlocal coupled NLS equation is constructed. By using the Darboux transformation, its soliton solutions are obtained. Dynamics and interactions of different kinds of soliton solutions are discussed.

Very recently, Ablowitz and Musslimani introduced a new integrable nonlocal nonlinear Schrodinger equation. In this paper, we investigate an integrable nonlocal modified Korteweg-de Vries equation (mKdV) which can be derived from the well-known AKNS system. We construct the Darboux transformation for the nonlocal mKdV equation. Using the Darboux transformation, we obtain its different kinds of exact solutions including soliton, kink, antikink, complexiton, rogue-wave solution, and nonlocalized solution with singularities. It is shown that these solutions possess new properties which are different from the ones for mKdV equation.

In this paper, the gauge equivalence between the modified Landau–Lifshitz equation and the perturbed defocusing nonlinear Schrodinger equation is proved from the perspective of geometry of given curvature condition. By using the gauge equivalence and the soliton perturbation theory of defocusing nonlinear Schrodinger equation, the first-order approximate 1-soliton solution to the modified Landau–Lifshitz equation is given.

The generalized coupled integrable dispersionless (CID) equation describes the current-fed string in a certain external magnetic field. In this paper, we propose a multi-component complex CID equation. The integrability of the multi-component complex equation is confirmed by constructing Lax pairs. One-soliton and two-soliton solutions are investigated to exhibit rich evolution properties. Especially, similar as the multi-component short pulse equation and the first negative AKNS equation, periodic interaction, parallel solitons, elastic and inelastic interaction, energy re-distribution happen between two solitons. Multi-soliton solutions are given in terms of Pfaffian expression by virtue of Hirota’s bilinear method.

Simple Summary The inclusion of Saccharomyces in the ration is beneficial to ruminants. We investigated the effects of inoculating a high-dose S. cerevisiae (108 cfu/g) on the nutritional composition and fermentation traits of sweet corn stalk. A high-dose S. cerevisiae inoculum increased the crude protein concentration of sweet corn stalk silage but decreased the silage quality. Thus, a high-dose S. cerevisiae inoculum is not conducive to obtaining high-quality corn stalk silage. Abstract This study examined the effects of a high-dose Saccharomyces cerevisiae inoculant alone or jointly with Lactobacillus plantarum on nutrient preservation, fermentation quality, and aerobic stability of sweet corn stalk silage. Fresh stalks (231 g dry matter (DM)/kg) were chopped and subjected to the following treatments: (1) deionized water (Uninoculated; U); (2) S. cerevisiae at 1 × 108 cfu/g of fresh forage (S); and (3) S. cerevisiae at 1 × 108 cfu/g plus L. plantarum at 1 × 105 cfu/g (SL). Treated stalks were ensiled in 5-litre laboratory silos for 30, 60, and 90 day. The S and SL silages had a greater (p < 0.001) pH and greater crude protein, ammonia nitrogen/total nitrogen, neutral detergent fibre, acid detergent fibre, and ethanol contents at all three ensiling periods than the U silage. Acetate, propionate and volatile fatty acids in the S and SL silages after 30 and 90 day of ensiling were greater (p < 0.05) than those in the U silage, but they were lower (p < 0.05) in the S and SL silages than in the U silage after 60 day. The lactate and V-score of the S and SL silages were lower (p < 0.001) than those of the U silage at all three ensiling periods. Compared with the U group, the aerobic stability of the S silage after 90 day of ensiling decreased (p < 0.05), and the aerobic stability of the SL silage was unaffected (p > 0.05). Overall, the quality of sweet corn stalk silage was not improved by inoculation with 108 cfu/g of S. cerevisiae alone or in combination with 1 × 105 cfu/g of L. plantarum.

In this paper, by employing the Hirota’s bilinear method, we construct the N -soliton solution for an integrable nonlocal discrete focusing nonlinear Schrodinger (dNLS + ) equation, and give the asymptotic analysis of two-soliton solution. The soliton solutions can be reduced to spatial periodic solution or singular solution by choosing the different parameters. Under continuous limit, the discrete soliton yields the one of nonlocal focusing nonlinear Schrodinger equation.

En s’appuyant sur les microdonnées du recensement canadien, cet article analyse les inégalités de revenus entre Canadiens de naissance et immigrants en provenance des pays en développement ainsi que la situation des immigrants sur le marché du travail. Nos résultats montrent clairement qu’il existe une disparité de revenus entre natifs, immigrants occidentaux et non occidentaux, et que cette disparité résulte des caractéristiques qui diffèrent entre ces trois groupes ainsi que de facteurs non observables tels que la discrimination. L’éducation n’a pas le même rendement pour tous les immigrants. La déqualification des immigrants est inégalement distribuée selon leur origine., Based on Canadian census microdata, this paper analyzes income inequality between native-born Canadians and immigrants from developing countries as well as discrimination against immigrants in the labor market. Our results clearly show that there is a disparity in income between the native-born and non-Western immigrants and that this disparity results from differences in characteristics between the three groups and unobservable factors, such as discrimination. Deskilling of immigrants is unequally distributed according to their origin.

Coupled dispersionless equation is an important model in quantum physics. Complex coupled dispersionless equation has valuable applications in geomerty. Recently, Ablowitz and Musslimani introduced and investigated a large class of reverse space, reverse time and reverse space-time nonlocal integrable equations. In this paper, we investigate a reverse space-time nonlocal complex coupled dispersionless equation, which was proposed in our paper [1]. By means of the Darboux transformation, we obtain its multi-soliton solutions from zero seed and nonzero seed. The asymptotic behavior of these solutions is discussed.

The hub-periphery development pattern of the Guangdong economy, to some extent, is a miniature of that of the Chinese economy. The Pearl River Delta, drawing from its first-nature comparative advantages in factor endowments and proximity to Hong Kong SAR, China, and Macau SAR, China, and the second-nature advantages as first-movers in the reforms in attracting and retaining domestic and foreign resources, has developed into a regional economic center. This paper examines the pattern of inter- and intra-provincial migration and that of the concentration of production, to explore the challenges and opportunities for the success of “double transfer.” The paper suggests a four-prong approach, to improve the business environment, support the realization of latent comparative advantages, increase the skill level of the labor force to support the upgrade of the production structure, and protect the vulnerable, to support the inclusive growth of the economy in Guangdong in a sustainable manner.

A semidiscrete Boussinesq system has been introduced by the means of recombination flows from a 4 × 4 spectral problem. We construct the Darboux transformation and explicit solutions for the semidiscrete Boussinesq system. We can find that the 1-fold Darboux-transformation solution of the system possesses more than one traveling waves. Especially, one of solutions comes into being two solitary waves after a period of time, which means that properties of solutions to semidiscrete integrable systems are richer than the ones in continuous integrable systems.

A new matrix spectral problem associated with sl(2,), which generalizes the Wadati-Konno-Ichikawa spectral problem, is introduced, and the corresponding hierarchy of soliton equations is generated from the associated zero curvature equations. A bi-Hamiltonian structure of the resulting generalized soliton hierarchy is furnished by using the trace identity, and thus, every system in the generalized hierarchy is Liouville integrable.

Integrable and nonintegrable discrete nonlinear Schrödinger equations (NLS) are significant models to describe many phenomena in physics. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time, and reverse space-time nonlocal integrable equations, including the nonlocal NLS equation, nonlocal sine-Gordon equation, nonlocal Davey-Stewartson equation, etc. Moreover, the integrable nonlocal discrete NLS has been exactly solved by inverse scattering transform. In this paper, we study a nonintegrable discrete nonlocal NLS, which is a direct discrete version of the reverse space nonlocal NLS. By applying discrete Fourier transform and modified Neumann iteration, we present its stationary solutions numerically. The linear stability of the stationary solutions is examined. Finally, we study the Cauchy problem for the nonlocal NLS equation numerically and find some different and new properties on the numerical solutions comparing with the numerical solutions of the Cauchy problem for the NLS equation.

A l'aide des micro-donnees confidentielles des recensements, ce travail examine les facteurs de l'inegalite de revenu et de la pauvrete des immigres au Canada des annees 1990 a 2006. Les resultats montrent que les immigres en provenance des pays en voie de developpement ont ete les plus atteints par les fluctuations economiques. Ils disposent en effet de revenus inferieurs a ceux des Canadiens de naissance et a ceux des immigres venus d'autres pays et, en sus, le rendement de leur capital humain a diminue entre 1991 et 2006. L'importance des flux migratoires venant des pays en voie de developpement a accru l'heterogeneite sociale de la population immigree, aggravant a la fois l'inegalite de revenu entre les immigres du Sud et les autres immigres, et parmi les premiers. Abstract: This paper is based on confidential data from some Censuses and examines the factors of inequality of earnings and of poverty relative to Canadian immigrants during the period of 1990 to 2006. The results of our analysis show that immigrants from developing countries have been the most harmed by economic fluctuations. They have less income than either native-born Canadians or immigrants from other countries; in addition, the return on their human capital has diminished between 1991 and 2006. The importance of migratory flux from developing countries has increased the social heterogeneity of the immigrant population, and has aggravated the inequality of income within the group of immigrants from the South as well as between them and other immigrants.

The multiple exp-function algorithm, as a generalization of Hirota’s perturbation scheme, is used to construct multiple wave solutions to the (3 + 1)-dimensional generalized KP and BKP equations. The resulting solutions involve generic phase shifts and wave frequencies containing many existing choices. It is also pointed out that the presented phase shifts for the two considered equations are all not of Hirota type.

In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.

Based on the contrast of survey method in existing railway, considering the actual situation on site, nuclear densimeter, Evd and light dynamic penetration methods were used in survey, and then analyze influencing factors of survey results in existing railway. Since there is no mathematical statistics method for survey evaluation in existing railway, taking "Quality inspection and evaluation standards for highway engineering" as reference, evaluation standard for existing railway at 200km/h was proposed. Filling materials segment method, task segment method and enforcement segment method were used for the evaluation in Ning-Qi existing railway, the road sections length that need reinforcement was reduced, which achieves good effect.

In this work, the crystallization of different silicon based thin films as the precursor of crystallization was investigated by femto-second laser with 800 nm wavelength. The linear absorption coefficient of a-Si films at that wavelength is quit lower than the other structures of Si-based thin film, which has no related with the incident light energy. However, we found that the crystallization of a-Si films was better than μc-Si films as the precursor. We use Z-scan techniques to prove that the two-photon absorption effect would be responsible for the crystallization. And unlike the linear absorption, the two-photon absorption effect is correlated with the incident light energy, as well as the micro-structure of the silicon based film. At the end of the paper, the crystallization by laser with wavelength longer than the absorption limit was discussed.

Nonlinear Schr\"odinger equation, short pulse equation and complex short pulse equation have important application in nonlinear optics. They can be derived from the Maxwell equation. In this paper, we investigate a coupled focusing-defocusing complex short pulse equation. The bright-bright, bright-dark and dark-dark soliton solutions of the coupled focusing-defocusing complex short pulse equation are given. Then the breathers are derived from the dark soliton solution. The rogue wave solutions are also constructed. The dynamics and the asymptotic behavior of the soliton solutions are analyzed, which reveals that there exist the elastic or inelastic collision in bright-bright soliton solution. But the interactions of bright-dark and dark-dark soliton solutions are both elastic., Comment: 26 pages, 16 figures

In this paper, we construct a new mixed function method for the first time. By using this new method, we study the two nonlinear differential-difference equations named the generalized Hybrid lattice and two-component Volterra lattice equations. Some new exact solutions of mixed function type such as discrete solitary wave solutions, discrete kink and anti-kink wave solutions and discrete breather solutions with kink and anti-kink character are obtained and their dynamic properties are also discussed. By using software Mathematica, we show their profiles.

La question de l’insertion sur le marche du travail urbain des migrants ruraux est aujourd’hui devenue essentielle en Chine. Dans un contexte de reformes economiques, les politiques migratoires en Chine continentale se sont redefinies, intensifiant ainsi fortement les migrations internes. Depuis les annees 1980, cet exode est pour l’essentiel celui des « paysans-ouvriers » (min gong), qui sont ainsi devenus un element majeur de la transition de la Chine vers une economie de marche. Cet article etudie l’insertion de ces migrants ruraux sur le marche du travail de la province du Guangdong a partir d’une base de donnees originale, issues d’une enquete sur les paysans-ouvriers, realisee en 2006. A partir de modeles de duree, nous portons une attention particuliere aux caracteristiques individuelles, temporelles (evolution de la mobilite dans l’emploi au cours du temps) et spatiales (role du lieu d’origine). Nos resultats montrent que les migrants forment un groupe heterogene du point de vue de leurs caracteristiques individuelles et de leur employabilite dans le delta de la riviere des Perles. Les femmes, les jeunes et les peu qualifies sont avantages. La proximite geographique est egalement favorable. Nous examinons enfin les determinants du salaire urbain des paysans-ouvriers qui s’inserent sur un marche du travail de plus en plus segmente et fragmente.

In this Letter, by considering two new ( 2 + 1 ) -dimensional discrete linear spectral problems, new ( 2 + 1 ) -dimensional integrable lattice hierarchies are constructed. It is shown that the two new ( 2 + 1 ) -dimensional integrable lattice hierarchies are extensions (to nonisospectral and ( 2 + 1 ) -dimensional cases) of a ( 1 + 1 ) -dimensional 3-field lattice hierarchy of Zhang et al. and a ( 1 + 1 ) -dimensional 2-field lattice hierarchy due to Merola, Ragnisco and Tu. We also obtain new ( 1 + 1 ) -dimensional nonisospectral lattice hierarchies which include a nonisospectral relativistic Toda lattice hierarchy.

PurposeThe purpose of this paper is to examine the efficiencies of China's foreign and domestic life insurance providers and to explore the relationship between ownership structure and the efficiencies of insurers while taking into consideration other firm attributes.Design/methodology/approachThe data envelopment analysis (DEA) method is used to estimate the efficiencies of the insurers based on a panel data between 1999 and 2004.FindingsThe results indicate that the average efficiency scores for all the insurers are cyclical. Both technical and scale efficiency reached their peaks in 1999 and 2000 and gradually reduced for the rest of the period under examination until 2004 when average efficiency were improved again. The Tobit regression results show that the insurers' market power, the distribution channels used and the ownership structures may be attributed to the variation in the efficiencies.Research limitations/implicationsBased on the research findings and the discussion, the study provides several recommendations for policy makers, regulators and senior executives of insurers.Practical implicationsThe research results highlight the importance of deregulating the sector to allow a further expansion of each individual insurer or encourage mergers and acquisitions of insurers so more efficient resource utilization can be achieved through economies of scale. It also suggests that it is imperative for insurers to recruit motivated insurance agents and offer them on‐the‐job training as a part of the management strategies for gaining technical efficiency.Originality/valueThe paper reports the development within China's insurance industry and is one of the few studies analyzing the efficiencies of China's insurers.

This paper examines the evolution of the size distribution of Chinese cities. Since the relaxation of restrictions on rural—urban migration in the 1980s, China has experienced rapid urban growth. However, cities of different sizes have experienced varying patterns of growth. First, the evolution of city size distribution in China is described by documenting the growth in city size and in the number of existing cities. Then, focusing on the period from 1990 to 2000, the urban evolutionary trend is analysed by means of the Pareto law estimation and the mobility of cities between different size groups is examined with the Markov transition matrix. The convergence hypothesis in the city population growth process is also tested. The results suggest that, contrary to the expected dominance of large city growth, the Chinese city size distribution evened out during the 1990s, with small cities growing more rapidly than large cities.

In this paper, we consider the (2+1)-dimensional discrete fourth-order nonisospectral problem. By using the Lax technique, three new (2+1)-dimensional nonisospectral four-field integrable lattice hierarchies are constructed. Their reductions yield three (1+1)-dimensional isospectral four-field integrable lattice hierarchies due to Mlaszak?Marciniak. We make a comparison between the (1+1)-dimensional discrete fourth-order nonisospectral problem and the third-order nonisospectral problem. We found that the integrable lattice hierarchies related to the discrete fourth-order nonisospectral problem have new characteristics.

In this Letter, we give a comment on [F. Yu, H. Zhang, Phys. Lett. A 353 (2006) 326]. We first show that there are many mistakes in the paper. The obtained 2 + 1 non-isospectral discrete integrable systems are not true. And then we reconstruct a 2 + 1 non-isospectral discrete integrable system by using the Lax technique, which is a generalization of the Blaszak–Marciniak lattice hierarchy.

In this paper, we will concentrate on the topic of integrable discrete hierarchies in 2+1 dimensions, and their connection with discrete Painleve hierarchies. By considering a (2+1)-dimensional nonisospectral discrete linear problem, two new (2+1)-dimensional nonisospectral integrable lattice hierarchies—the 2+1 nonisospectral relativistic Toda lattice hierarchy and the 2+1 nonisospectral negative relativistic Toda lattice hierarchy—are constructed. It is shown that the reductions of the two new 2+1 nonisospectral lattice hierarchies lead to the (2+1)-dimensional nonisospectral Volterra lattice hierarchy and the (2+1)-dimensional nonisospectral negative Volterra lattice hierarchy. We also obtain two new (1+1)-dimensional nonisospectral integrable lattice hierarchies and two new ordinary difference hierarchies which are direct reductions of the two 2+1 nonisospectral integrable lattice hierarchies. One of the two difference hierarchies yields our previously obtained generalized discrete first Painleve (dPI) hierarchy and another one yields a generalized alternative discrete second Painleve (alt-dPII) hierarchy.

In this paper, we try to understand the geometry for a nonlocal nonlinear Schrodinger equation (nonlocal NLS) and its discrete version introduced by Ablowitz and Musslimani, Phys. Rev. Lett. 110, 064105 (2013); Phys. Rev. E 90, 042912 (2014). We show that, under the gauge transformations, the nonlocal focusing NLS and the nonlocal defocusing NLS are, respectively, gauge equivalent to a Heisenberg-like equation and a modified Heisenberg-like equation, and their discrete versions are, respectively, gauge equivalent to a discrete Heisenberg-like equation and a discrete modified Heisenberg-like equation. Although the geometry related to the nonlocal NLS and its discrete version is not very clear, from the gauge equivalence, we can see that the properties between the nonlocal NLS and its discrete version and NLS and discrete NLS have significant difference. By constructing the Darboux transformation for discrete nonlocal NLS equations including the cases of focusing and defocusing, we derive their discrete soliton solutions, which differ from the ones obtained by using the inverse scattering transformation.

In this article, by considering a 2 + 1 dimensional discrete non-isospectral linear problem, a new 2 + 1 dimensional integrable lattice hierarchy is constructed. It is shown that a generalization of the discrete second Painleve hierarchy can be obtained as a reduction. Other reductions include new 1 + 1 dimensional integrable lattice hierarchies.

Le Canada a connu, au cours des dernieres decennies, une importante augmentation de sa population immigrante. Cette augmentation ne s’est pas produite sans tensions ni questionnements quant a la forme que devaient prendre les institutions de la societe d’accueil. Une partie de la reponse instituiionnelle a ete apportee par l’adoption d’une politique du multiculturalisme en 1971 et par la constitutionnalisation des droits fondamentaux et individuels. Le Canada a ainsi enregistre un certain succes quant a l’adaptation de la democratie liberale a cet afflux de nouveaux arrivants, la gestion de la diversite et l’energence d’une identite inclusive commune. Ce succes reste cependant a evaluer sur le plan de la lutte contre la discrimination et les inegalites. Cette evaluation a deja ete entamee dans le domaine de l’emploi, mais reste a poursuivre dans celui du logement. C’est ce que cet article propose en procedant a une analyse de la decomposition des ecarts de la qualite de logement entre non-immigrants et immigrants pour trois regions metropolitaines du Canada. La qualite logement est mesuree par le nombre moyen de pieces par personne et est mise en relation avec des variables sociodemographiques, socioeconomiques et caracterisant l’immigration. Les resultats indiquent une convergence entre les trois grandes metropoles canadiennes et soulignent clairement l’existence d’une difference dans la qualite de logement entre non-immigrants et immigrants.

In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula.