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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

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.

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.

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.

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.

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.

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.

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 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.

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.

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 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.

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.

In this Letter, by means of considering matrix form of a new Schrodinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples.

In this Letter, by means of the matrix Lax representations for two Blaszak–Marciniak three-field lattice hierarchies, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved density and the associated flux formulaically.

In this Letter, by means of new matrix Lax representation for the Blaszak–Marciniak four-field integrable lattice hierarchy, we demonstrate the existence of infinitely many conservation laws for the lattice hierarchy and give the corresponding conserved density and the associated flux formulaically. So, its integrability is further confirmed.

Using survey data from China, this article examines the effects of income gaps on migration decisions and the sources of these gaps. The econometric results support the hypothesis that income gaps significantly influence migration decisions. When income gap reaches a certain level, the reaction of the migration probability to income gap is weaker for men than for women. The relative income of women is less sensitive to an increase in rural income but more sensitive to a decrease in urban income than that of men. Moreover, we find that the urban to rural income gap is larger for women than for men, which suggests that women receive larger monetary return from migration than men do. In decomposing income gaps, we find that the gap for men is largely determined by differences in the attributes of migrants and nonmigrants, whereas for women, the gap is mainly determined by differences in returns to attributes.

Large numbers of agricultural labor moved from the countryside to cities after the economic reforms in China. Migration and remittances play an important role in transforming the structure of rural household income. This article examines the impact of rural-to-urban migration on rural poverty and inequality in a mountainous area of Hubei province using the data of a 2002 household survey. Since migration income is a potential substitute for farm income, we present counterfactual scenarios of what rural income, poverty, and inequality would have been in the absence of migration. Our results show that, by providing alternatives to households with lower marginal labor productivity in agriculture, migration leads to an increase in rural income. In contrast to many studies that suggest that the increasing share of nonfarm income in total income widens inequality, this article offers support for the hypothesis that migration tends to have egalitarian effects on rural income for three reasons: (1) migration is rational self-selection--farmers with higher expected return in agricultural activities and/or in local nonfarm activities choose to remain in the countryside while those with higher expected return in urban nonfarm sectors migrate; (2) households facing binding constraints of land supply are more likely to migrate; (3) poorer households benefit disproportionately from migration.

This paper examines the growth performance and income inequality in eight Chinese provinces during the period of 1989–2004 using the China Health and Nutrition Survey data. It shows that income grew for all segments of the population, and as a result, poverty incidence has fallen. However, income growth has been uneven, most rapidly in coastal areas, and among the educated. A decomposition analysis based on household income determination suggests that income growth can largely be attributed to the increase in returns to education and to the shift of employment into secondary and tertiary sectors.

Using data from the Survey of Labour and Income Dynamics (SLID) – we analyze non-employment episodes for immigrants from developing countries and compare their situation to that of immigrants from more developed countries and Canadian-born individuals between 1996 and 2006. The methods used allowed us to draw the following conclusion: significant differences exist between these three groups in the labour market mobility, the average duration of a non-employment episode, and the factors that affect the propensity to exit from a non-employment episode. These differences demonstrate a particular disadvantage for immigrants from developing countries. In fact, they tend to spend more time in non-employment episodes compared to their counterparts from the more developed countries and compared to Canadian-born individuals.

By using new Lax pairs, we prove that the continuous limits of the gauge equivalent structures of the discrete nonlinear Schrodinger equation for κ=1 and −1 are exactly the classical ones of the nonlinear Schrodinger equation for κ=1 and −1 respectively.

From a proper 2 × 2 discrete isospectral problem, a new differential-difference integrable equation in Lax sense is proposed by a discrete zero curvature equation. The DDKdV (differential-difference DdV equation) proposed by Ohta and Hirota and DDCDGKS (DD Caudrey-Dodd-Gibbon-Kotera-Sawada equation) are rederived. Some other new discrete KdV equations, discrete mKdV equations and discrete high order KdV equations which converge to the corresponding continuous soliton equations in the continuum limit are obtained. Integrable time discretizations of the DDKdV, DDmKdV (differential-difference mKdV equation) and DDHOKdV (differential-difference high order KdV equations) are given.

A (2 m + 1)th-order generalized KdV equation is considered, where m is a positive integer. Four new explicit travelling solitary-wave solutions are obtained for the case m = 4. The case of arbitrary m ≥ 3 is considered; it is shown that, subject to certain restrictions on the coefficients in the equation, there are always at least two sech-polynomial type solutions.

Some new Lax integrable hierarchies associated with 3 × 3 matrix spectral problems and their bi-Hamiltonian structures are obtained.

With the help of a commutativity condition, we construct the general KP equation with explicit x, y and t dependence, the Lax pair for the equation and the general MKP equation with explicit x, y and t dependence are obtained.

In this paper, we give the Painleve property, Backlund transformation, Lax pair and soliton-like solution for a variable coefficient KP equation.

In this paper, we obtain the Lax pair, Backlund transformation, solitary wave solution and infinite conservation laws of the general KP equation and MKP equation with variable coefficients.