Search Results (180)

This study examines a nonlinear partial differential equation, namely the (3+1)-dimensional Boussinesq-type equation. To explore this model, three versatile analytical approaches are applied: the Exp-function method, the Kudryashov method, and the Riccati equation method. Using these techniques, a range of exact analytical solutions is derived, exhibiting diverse structural forms such as periodic, kink-type, rational, and trigonometric solutions. The analysis reveals the rich dynamical behavior of the equation and demonstrates its effectiveness in modeling a variety of nonlinear wave phenomena across different physical contexts. Several of the obtained solutions are illustrated through graphical representations for better interpretation. The results include hyperbolic, trigonometric, and rational function solutions, along with a sensitivity analysis. To highlight the physical relevance of the findings, suitable parameter values are selected, and the corresponding wave behaviors are visualized using three-dimensional and contour plots generated with Maple 2024. Overall, the study provides valuable insights into the mechanisms underlying the generation and propagation of complex nonlinear phenomena in fields such as fluid dynamics, optical fiber systems, plasma physics, and ocean wave transmission. Full article

This paper focuses on a high-order Korteweg–de Vries wave equation. The extended F-expansion method, a modified form of Kudryashov’s auxiliary equation approach, is employed to construct Jacobi elliptic function solutions for this equation. Three distinct families of solutions are obtained, including solitary waves, breathers, dark/bright solitons, bright–dark interaction solitons, and rogue-like solutions. To better illustrate the complex nonlinear dynamics of the high-order Korteweg–de Vries wave equation, representative solutions are selected, and their moduli are visualized using Maple software through three-dimensional, two-dimensional, and contour plots. Full article

The Kudryashov–Sinelshchikov equation (KSE) is crucial in modeling pressure waves in liquids containing gas bubbles, capturing both nonlinear wave phenomena and dispersion effects. This article applies the reproducing kernel Hilbert space method (RKHSM) to find a numerical solution for the time-fractional KSE. We develop a numerical solution to the KSE using the RKHSM, which offers an efficient and accurate approach for solving nonlinear partial differential equations due to its smoothness and orthogonality properties. The key components of this method include the reproducing kernel (RK) theory, important Hilbert spaces, normal basis, orthogonalization, and homogenization. We construct an appropriate RK and derive an iterative solution that converges rapidly to the exact solution. The effectiveness of this approach is demonstrated through numerical simulations in which we analyze the behavior of pressure waves and compare the results with existing analytical and numerical solutions. The RKHSM consistently demonstrates highly accurate, rapid convergence, and remarkable stability across a wide range of problems. Thus, the RKHSM is a promising tool for studying wave propagation in bubbly liquids. Full article

A comprehensive investigation was conducted on high-hafnium zircons from the LCT (Li-Cs-Ta) pegmatites of the Vasin-Mylk rare-metal deposit within the Fennoscandian Shield. In situ analysis of trace element composition and oxygen isotope ratios were performed using secondary ion mass spectrometry (SIMS), complemented by internal structural examination via scanning electron microscopy (SEM). The research focuses on deciphering compositional zoning within zircon crystals and characterizing their geochemical signatures to constrain crystallization conditions. The study revealed anomalously high concentrations of Hf (up to 381,000 ppm) and Li (up to 152 ppm), paired with extremely low abundances of U (~10 ppm) and total rare earth elements (~35 ppm). Marked geochemical contrasts were identified between the central and rim domains of the zircons. Central zones display well-fractionated rare earth element (REE) patterns featuring positive Ce and negative Eu anomalies, while the high-Hf rims exhibit weakly differentiated spectra with variable Ce anomalies. The identified W-type tetrad effect suggests crystallization from a melt strongly influenced by coexisting fluids. The obtained δ¹⁸O values are consistent with a mantle source and suggest crystallization within a system closed to external fluids. The zircons from the Vasin-Mylk deposit crystallized during the transitional period between the late magmatic and early hydrothermal stages of a highly differentiated pegmatite system. These results contribute to a better understanding of ore genesis in LCT pegmatite systems. Full article

In this study, we present a unified symmetry-conservation solution analysis of a well-posed resonant nonlinear Schrödinger (NLS)-type equation incorporating spatio-temporal dispersion and inter-modal dispersion. Working within the truncated M-fractional derivative framework, we first construct exact traveling-wave solution families via the Kudryashov expansion method, together with the corresponding parameter constraints and limiting cases. We then determine the admitted Lie point symmetries and establish the associated Lie algebra, including the commutator structure, adjoint representation, and an optimal system of one-dimensional subalgebras for classification. Using the conservation theorem, we derive conserved vectors associated with the fundamental invariances of the model; in the NLS setting and under suitable conditions, these quantities can be interpreted as generalized power (mass), momentum, and energy-type invariants. Overall, the results provide explicit wave profiles and structural invariants that enhance the interpretability of the model and offer benchmark expressions useful for further qualitative, numerical, and stability investigations in nonlinear dispersive wave dynamics. Full article

The current paper retrieves implicit quiescent soliton solutions to optical metamaterials with nonlinear chromatic dispersion with generalized temporal evolution. Seven forms of self-phase modulation structures, as proposed by Kudryashov with time, are taken up. The implemented integration algorithm is Lie symmetry. A few of the solutions are in quadratures, while others are in terms of special functions. We also characterize the parameters that constrain the existence of such solutions. Full article

This study investigates the conformable nonlinear Schrödinger equation (NLSE) with self-phase modulation (SPM) and Kudryashov’s generalized refractive index, crucial for pulse propagation in optical fibers. By applying the modified simplest equation method, we derive several novel soliton solutions and investigate their dynamic behavior within the NLSE framework enhanced with a conformable derivative. The governing conformable NLSE also exhibits symmetry patterns that support the structure and stability of the constructed soliton solutions, linking this work directly with symmetry-based analysis in nonlinear wave models. Furthermore, various graphs are presented through 2D, 3D, and contour plots. These visualizations highlight different soliton profiles, including kink-type, wave, dark, and bell-shaped solitons, showcasing the diverse dynamics achievable under this model, influenced by SPM and Kudryashov’s generalized refractive index. The influence of the conformable parameter and temporal effects on these solitons is also explored. These findings advance the understanding of nonlinear wave propagation and have critical implications for optical fiber communications, where managing pulse distortion and maintaining signal integrity are vital. Full article

High-risk human papillomavirus (HPV) is the leading etiological factor in cervical cancer, creating a pressing need for less invasive and more objective diagnostic tools. This pilot study pioneers the application of Raman spectroscopy to cell-free cervicovaginal lavage (CVL) for distinguishing between low-grade and high-grade squamous intraepithelial lesions (LSIL and HSIL) in HPV-positive patients. Raman spectra were acquired at 532-nm excitation from cell-free CVL samples of 20 patients with histologically confirmed LSIL (n = 9) or HSIL (n = 11). Comparative analysis of Raman bands revealed a significant biochemical shift in HSIL, presumably characterized by reduced glycogen and lactate/lactic acid levels alongside substantially elevated heme proteins. A diagnostic model based on key spectral intensity ratios achieved differentiation between LSIL and HSIL with 80% sensitivity and 86% specificity. These findings demonstrate that Raman spectroscopy of cell-free CVL effectively captures profound metabolic and microvascular alterations characteristic of neoplastic progression, showcasing its strong potential as a rapid, cost-effective, non-invasive, and objective tool for cervical lesion risk stratification. Full article

Kazakhstan’s asbestos industry produces over 3 million tons of waste annually. The primary component of asbestos ore waste (AOW) is magnesium rich minerals. In this study, the extraction of magnesium from AOW with nitric acid (HNO₃) was for the first time systematically studied. A series of experiments were conducted to optimize acid concentration (300–600 g/L), leaching temperature (55–95 °C), leaching time (60–180 min), solid-to-liquid ratio (1:3–1:7), and particle size, with the overall goal of maximizing magnesium extraction and cost efficiency. Our results provide dependence of magnesium extraction in the order of acid concentration  >  temperature  >  time  >  solid-to-liquid ratio, while particle size was found to be negligible. The cost-efficiency optimization demonstrated the positive impact of the relatively low acid concentrations (< 450 g/L) and temperatures between 65 and 85 °C, while the Protodyakonov model validated a linear dependence of the extraction rate on temperature and acid concentration. Our model demonstrates that extraction efficiencies of up to 90% can be achieved while reducing reagent use and lowering the overall cost of magnesium production. Leaching of magnesium by HNO₃ also opens a pathway to a closed-cycle process, due to the formation of magnesium nitrate. The thermal decomposition of Mg(NO₃)₂ provides valuable products such as MgO and NO₂ reused in HNO₃ regeneration for subsequent cycles. The proposed model predicts magnesium extraction from asbestos ore depending on leaching parameters with reasonable accuracy. Full article

Bile acids, the primary components of bile, are cholesterol-derived molecules synthesized in the liver and secreted to the small intestine. Besides their primary digestive roles, bile acids have antimicrobial properties and serve as an environmental cue for intestinal pathogens, modulating the expression of virulence factors, e.g., toxins and effector proteins. Whereas timely recognition and neutralization of pathogenic toxin effectors by the host is critical, our understanding of the effects of bile on their structure and function is limited. In this work, we found that bile effectively protected cultured IEC-18 enterocytes from the mixture of Aeromonas hydrophila secreted toxins, containing hemolysin, aerolysin, and RtxA (MARTX). To explore whether these effects have broad specificity, we employed biochemical and biophysical techniques to test the in vitro effects of bile and bile acids on several effector domains of MARTX and VgrG toxins from Vibrio cholerae and Aeromonas hydrophila, and catalytic domains of TcdA and TcdB toxins from Clostridioides difficile. Bile compromised the structural integrity of the tested effectors to various degrees in a protein charge-dependent manner. Bile and bile acids promoted exposure of hydrophobic residues and the unfolding of most, but not all, of the tested effectors, facilitating their precipitation and cleavage by chymotrypsin. Bile also inhibited specific activities of the tested effector enzymes, partially due to imposed oxidation of their catalytic residues. To summarize, this work validated bile as a non-proteinaceous factor of innate immunity, capable of compromising the structural integrity and function of the effector domains of various bacterial toxins. Full article

Avian influenza viruses (AIV) cause severe economic losses in poultry production and pose zoonotic threats, necessitating rapid, field-deployable diagnostics. While real-time PCR is the gold standard, its use is limited in resource-constrained settings. This study aimed to develop and validate optimized loop-mediated isothermal amplification (LAMP) protocols for AIV detection directly at sample collection sites. We optimized Real-Time RT-LAMP and colorimetric LAMP assays targeting the conserved M gene, using primers described in the literature. Analytical sensitivity was assessed with a plasmid standard (10⁶–10⁰ copies/μL); specificity was evaluated against 27 AIV strains (H1–H12) and heterologous avian viruses (Newcastle disease, infectious bronchitis, Gumboro, and laryngotracheitis viruses). Reverse transcription was integrated into the LAMP reaction. Real-Time LAMP with SYBR Green achieved 100% analytical sensitivity (95% CI: 80–100; detection limit: Ct = 38), while colorimetric LAMP (cresol red, malachite green, calcein) detected 10² plasmid copies (Ct = 32) with 91.67% sensitivity (95% CI: 76.1–100). No cross-reactivity occurred. These optimized LAMP protocols offer sensitivity and specificity comparable to PCR, require minimal equipment, and enable rapid AIV screening, significantly enhancing early detection and epidemiological surveillance in field conditions. Full article

This work addresses the Cauchy problem for a linear equation with a first-order time derivative t and an arbitrary-order spatial derivative x. This equation is a generalization of the linear heat equation of the second order in the case of arbitrary order with respect to spatial variable. The considered linear equation arises from the linearization of the Burgers hierarchy of equations. The Cauchy problem to a linear equation can be solved using the Green function method. The Green function is explicitly constructed for the case of dissipative and dispersive equations and is expressed in terms of generalized hypergeometric functions. The general formulas obtained for representing Green’s function are new. A discussion of specific cases of the equation is also provided. Full article

This paper provides highly dispersive optical soliton solutions to the perturbed complex Ginzburg–Landau equation. The self-phase modulation structures are maintained in three forms, which are derived from the power law of nonlinearity with arbitrary intensity. The paper employs the semi-inverse variational principle as its integration scheme, as conventional methods are incapable for it. The amplitude–width relation of the solitons is reconstructed by employing Cardano’s method to solve a cubic polynomial equation. Also presented are the necessary parameter constraints that naturally arise from the scheme. These findings enhance our understanding of soliton dynamics and pave the way for further research into more complex nonlinear systems. Future studies may explore the implications of these results in various physical contexts, potentially leading to novel applications in fields such as fiber optics and quantum fluid dynamics. Full article

This paper investigates quiescent solitons in optical fibers and crystals, modeled by the complicated Ginzburg–Landau equation incorporating nonlinear chromatic dispersion and six self-phase modulation structures introduced by Kudryashov. The model is formulated with linear temporal evolution and analyzed using Lie symmetry methods. The study also identified parameter constraints under which solutions exist. Full article

The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the $(G^{\prime }/G)$ expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article