In this study, using the Kudryashov
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function method and the generalized Kudryashov method, the
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-dimensional resonant nonlinear Schrödinger equation with dual-power law nonlinearity has ...been effectively examined for finding optical soliton solutions. The Kudryashov
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function technique has numerous advantages that make symbolic computing considerably simpler, particularly while dealing with strongly dispersive nonlinear equations. The generalised Kudryashov method is noteworthy due to its capacity to address a wide range of complex nonlinear ordinary differential equations (NLODEs) observed in diverse engineering, scientific and mathematical fields. Newly generated nonlinear Schrödinger equation is demonstrated by the resonant nonlinear Schrödinger equation used to describe nonlinear optical phenomena. In order to achieve the goal, the governing model was first transformed into a NLODE, and then the solution sets and solution functions were derived based on the definitions of the suggested approaches. Solitons are localized wave forms that retain their shape and stability as they propagate across optical fiber. Optical solitons are characterized by their ability to maintain their shape and amplitude during propagation, even when encountering other solitons. Using the suggested approaches, the singular, dark, kink-antikink and bright soliton solutions from the governing equation have been extracted. Under the appropriate selection of parameter values, 3D, 2D and contour graphs are shown to illustrate the physical characteristics of the obtained results. All generated solutions are demonstrated to be analytically stable by the analysis of modulation instability, which also reveals the stability and movement of the waves. These solutions have extensive implications in the field of telecommunications and nonlinear fiber optics and assist in understanding the physical phenomena underlying the equation. These methods are new and standardised, and they can be applied to solve a variety of mathematical and physical problems.
Hyperspectral remote sensing (Hyperion EO-1) data has emerged as most promising tool in quantifying severity of salt-affected soils. The study deals with identifying sensitive spectral bands ...(wavelength regions) for salinity parameters and thereafter used to compute spectral indices viz. Salinity index (SI), Brightness index (BI), Normalized Differential Salinity Index (NDSI), Combined Spectral Response Index (COSRI) and Coloration index (CI). Six sensitive hyperspectral bands (Band 9, 20, 22, 28, 29 and 46) of Hyperion-1 satellite data were identified to generate the spectral indices. The relationship between these spectral indices and salinity parameters of electrical conductivity (EC), sodium adsorption ratio (SAR) and exchangeable sodium percentage (ESP) were established to generate maps showing severity of salt-affected soils of the area. The severity maps were categorized into classes of normal, slight, moderate and highly showing the spatial distribution of severity of salt affected soils. Among these spectral indices, SI shown highest correlation coefficient (r²) with the parameters of ECe (r² = 0.777), SAR (r² = 0.801) and ESP (r² = 0.804) followed by BI, COSRI and CI. The Hyperion data has shown the potential to assess severity of salt-affected soils for large area which may very useful for identifying the area for carring out reclamation measures and management planning.
The mathematical modeling of physical systems is generally governed by evolution equations in nonlinear form. Therefore, it is critical to obtain exact analytical solutions to these equations. This ...paper contains the application of improved (G′/G)-expansion and extended (G′/G)-expansion methods for establishing new analytical solutions of a nonlinear evolution equation. Mainly, improved (G′/G)-expansion and extended (G′/G)-expansion methods have been applied to time-fractional Kaup-Kupershmidt equation for getting some new general forms of exact solutions. Here, algorithms provide a more convenient and systematically handling the solution process of the non-linear evolution equations.
In this article, the generalized Kudryashov method is used to investigate the exact solutions of the time-fractional perturbed nonlinear Schrödinger equation with a truncated M- fractional ...conformable derivative, as well as the Kerr law and power law of nonlinearity. In mathematical physics and engineering, this equation has a wide range of applications. By using the travelling wave transformation with these two nonlinearities, this governing equation has been transformed to a nonlinear ordinary differential equation, and then the very powerful and efficient method viz. the generalized Kudryashov approach has been applied in the resulting equation to obtain optical soliton solutions. These solutions can be useful and desired for illuminating certain nonlinear physical phenomena in truly nonlinear dynamical systems. This study successfully constructs kink singular, singular soliton, bright, dark, and combined dark-bright optical singular soliton solutions.The physical meaning of 2D and 3D geometrical structures for certain derived solutions has been described here by assigning specific values to the undefined parameters, and it demonstrates the physical configurations of the obtained solutions.
In the present article, the new exact solutions of time-fractional coupled Drinfeld–Sokolov–Wilson equations have been derived by using a new reliable analytical method. We applied a comparatively ...new method, viz. Jacobi elliptical function method, for finding some new exact solutions of time-fractional coupled Drinfeld–Sokolov–Wilson equations. The fractional complex transform has been used here along with the property of local fractional calculus for reduction of fractional partial differential equations to ordinary differential equations. The obtained results have been plotted here for demonstrating the nature of the solutions.
The main objective of this paper is to introduce a collocation-based method for solving a system of two-dimensional Volterra integral equations. The proposed approach is based on the Jacobi wavelets ...collocation procedure. In addition, the Gegenbauer wavelets method has been implemented to show the comparison of error norms obtained by the proposed method. This proposed approach is applied to reduce the system of Volterra integral equations into a system of algebraic equations. Furthermore, some theorems are elucidated to establish the convergence analysis of the proposed method. Some numerical problems are presented in order to show the accuracy and effectiveness of the proposed scheme. Furthermore, comparison tables and some figures are depicted in support of numerical analysis of the proposed scheme.
Climate and weather directly impact plant phenology, affecting airborne pollen. The objective of this systematic review is to examine the impacts of meteorological variables on airborne pollen ...concentrations and pollen season timing. Using PRISMA methodology, we reviewed literature that assessed whether there was a relationship between local temperature and precipitation and measured airborne pollen. The search strategy included terms related to pollen, trends or measurements, and season timing. For inclusion, studies must have conducted a correlation analysis of at least 5 years of airborne pollen data to local meteorological data and report quantitative results. Data from peer-reviewed articles were extracted on the correlations between seven pollen indicators (main pollen season start date, end date, peak date, and length, annual pollen integral, average daily pollen concentration, and peak pollen concentration), and two meteorological variables (temperature and precipitation). Ninety-three articles were included in the analysis out of 9,679 articles screened. Overall, warmer temperatures correlated with earlier and longer pollen seasons and higher pollen concentrations. Precipitation had varying effects on pollen concentration and pollen season timing indicators. Increased precipitation may have a short-term effect causing low pollen concentrations potentially due to “wash out” effect. Long-term effects of precipitation varied for trees and weeds and had a positive correlation with grass pollen levels. With increases in temperature due to climate change, pollen seasons for some taxa in some regions may start earlier, last longer, and be more intense, which may be associated with adverse health impacts, as pollen exposure has well-known health effects in sensitized individuals.
Crossbreeding is a strategy to counter the declining fertility, resilience, and longevity of purebred Holstein (Ho) cows. However, little is known of the effects of long-term systematic rotational ...crossbreeding on milk technological properties and cheese yield (CY). In this study, we compared the individual milk composition, milk coagulation properties (MCP), and CY of 468 purebred Ho and 648 crossbred (CR) cows obtained from two 3-breed rotational crossbreeding systems using Viking Red (VR), Montbéliarde (Mo), and Ho sires over 4 generations. Individual milk samples were collected once from 1,116 primiparous and multiparous cows kept in 2 dairy herds, raised for the production of Grana Padano (high milk yield, total mixed ration based on corn silage) and Parmigiano Reggiano (moderate milk yield, only dry feeds) cheeses. In both herds, a 3-breed rotational mating system was used in which Ho cows were first inseminated with VR, whereas Mo and Ho semen was used in the subsequent generations. In one herd, the sequence Mo-VR-Ho was also used. Individual milk samples were analyzed for milk composition, single-point MCP, and parameters for modeling curd firming over time, whereas CY and milk nutrient recovery in the curd were assessed through a laboratory cheese-making procedure. Compared with Ho, CR cows produced 5.8% less milk, which had comparable fat but greater protein and casein contents and lower lactose contents and somatic cell scores. Milk from CR cows tended to reach a curd firmness of 20 mm more quickly and exhibited greater curd firmness at 45 and 60 min from rennet addition. Holstein and CR cows yielded milk with similar CY and recovery in the curd traits. The milk fat content, somatic cell scores, curd firmness traits, and CY of CR cows relative to the Ho cows differed in the 2 herds, and the favorable effects on the CR cows were more evident in the herd with the greatest milk yield and the worst MCP traits. Crossbred cows of the 4 generations performed similarly, with the exception of the better MCP of the milk from first-generation CR cows. The 2 rotational systems using different sire-breed sequences also performed similarly. In summary, both rotational crossbreeding programs exhibited some advantage over the Ho purebred breeding system in terms of milk composition and MCP but not CY. Future research is needed to investigate the interactions between crossbreeding schemes and dairy systems.
Oleofoams are dispersions of gas bubbles in a continuous oil phase and can be stabilized by crystals of fatty acids or waxes adsorbing at the oil-air interface. Because excess crystals in the ...continuous phase form an oleogel, an effect of the bulk rheology of the continuous phase is also expected. Here, we evaluate the contributions of bulk and interfacial rheology below and above the melting point of a wax forming an oleogel in sunflower oil. We study the dissolution behaviour of single bubbles using microscopy on a temperature-controlled stage. We compare the behaviour of a bubble embedded in an oleofoam, which owes its stability to both bulk and interfacial rheology, to that of a bubble extracted from the oleofoam and resuspended in oil, for which the interfacial dilatational rheology alone provides stability. We find that below the melting point of the wax, bubbles in the oleofoam are stable whereas bubbles that are only coated with wax crystals dissolve. Both systems dissolve when heated above the melting point of the wax. These findings are rationalized through independent bulk rheological measurements of the oleogel at different temperatures, as well as measurements of the dilatational rheological properties of a wax-coated oil-air interface.
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