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Understanding the intricate Korteweg–de Vries ( c K d V ) equation is paramount for comprehending various nonlinear wave phenomena, owing to its capacity to depict the propagation of nonlinear waves in media characterized by complex-valued dispersive and nonlinear coefficients. The practical ramifications of the c K d V equation are extensive, spanning disciplines such as optics, plasma physics, and other realms dealing with intricate media. This investigation employs the Khater II method and a generalized rational approach as analytical methodologies to generate novel exact solutions for the c K d V equation. The Khater II method is employed to transform the nonlinear partial differential equation into a nonlinear ordinary differential equation, thus facilitating a systematic resolution. Moreover, the generalized rational technique utilizes a rational ansatz function to derive diverse forms of solutions. Application of these methodologies leads to the discovery of fresh exact solutions, encompassing solitary and periodic wave solutions for the c K d V equation. These solutions are expressed in rational forms featuring arbitrary functions, thereby expanding the repertoire of known solutions for the model. The efficacy of the analytical methodologies employed becomes evident through the discovery of these novel exact solutions, thereby enriching our understanding of the physical interpretations and wave characteristics associated with the c K d V equation. The derived solutions augment the existing body of knowledge pertaining to the model. This research enhances our comprehension of the c K d V equation, thereby advancing nonlinear wave analysis with potential applications in physics, optics, plasma science, and allied engineering domains. Future investigations may explore the extension of these methodologies to address other nonlinear wave equations. [ABSTRACT FROM AUTHOR]

This study delves into investigating the stability of solutions pertaining to the generalized Davey–Stewartson ( D S ) equation by employing the generalized rational method and projective Riccati equations method within the Hamiltonian system framework. The central focus lies in unraveling the physical significance of this model within the realm of plasma physics, shedding light on its intricate connections with analogous equations. The generalized D S equation, a pivotal nonlinear evolution model, serves as a vital tool in comprehending the evolution of coupled waves across various physical systems, notably within the domains of fluid dynamics and plasma physics. Its significance lies in its capacity to elucidate the intricate interplay among different wave components, offering a holistic perspective on wave interactions within plasma mediums. Through the meticulous application of rigorous analytical methods, this investigation uncovers pivotal insights into the stability of solutions, thereby enriching our understanding of mathematical models in plasma physics. The findings presented in this research contribute significantly to advancing the understanding of nonlinear dynamics, with profound implications for future exploration in plasma physics and related fields. In essence, this study underscores the analytical prowess of the generalized rational and projective Riccati equations methods, accentuating their relevance and applicability to the generalized D S equation and, by extension, their role in enhancing our comprehension of coupled wave phenomena within diverse plasma systems. [ABSTRACT FROM AUTHOR]

This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible S (t) , infected I (t) , treated T (t) , and recovered R (t) with the susceptible category further divided into two subcategories S 1 (t) and S 2 (t) . In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

This manuscript introduces a novel bidirectional wave dynamics to the q-deformed Sinh-Gordon model. The main objective of this study is to investigate the simultaneous motion of two symmetrical waves. The ϕ 6 -model expansion technique is used for achieving the required objective. The ϕ 6 -model expansion technique extracts new solitary wave solutions for the proposed model. Moreover, we delve into the mathematical aspects and explore the physical characteristics of the q-deformed Sinh-Gordon equation in its bidirectional form. The study provides intricate derivations of the innovative solutions, accompanied by visual representations that offer insights into their physical structures. The findings of this investigation significantly contribute to our comprehension of this model. Finally, fascinating three-dimensional plots and two-dimensional line plots are displayed. [ABSTRACT FROM AUTHOR]

The cultivation of grapes encounters various challenges, such as the presence of pests and diseases, which have the potential to considerably diminish agricultural productivity. Plant diseases pose a significant impediment, resulting in diminished agricultural productivity and economic setbacks, thereby affecting the quality of crop yields. Hence, the precise and timely identification of plant diseases holds significant importance. This study employs a Convolutional neural network (CNN) with and without data augmentation, in addition to a DCNN Classifier model based on VGG16, to classify grape leaf diseases. A publicly available dataset is utilized for the purpose of investigating diseases affecting grape leaves. The DCNN Classifier Model successfully utilizes the strengths of the VGG16 model and modifies it by incorporating supplementary layers to enhance its performance and ability to generalize. Systematic evaluation of metrics, such as accuracy and F1-score, is performed. With training and test accuracy rates of 99.18 and 99.06%, respectively, the DCNN Classifier model does a better job than the CNN models used in this investigation. The findings demonstrate that the DCNN Classifier model, utilizing the VGG16 architecture and incorporating three supplementary CNN layers, exhibits superior performance. Also, the fact that the DCNN Classifier model works well as a decision support system for farmers is shown by the fact that it can quickly and accurately identify grape diseases, making it easier to take steps to stop them. The results of this study provide support for the reliability of the DCNN classifier model and its potential utility in the field of agriculture. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas" published in Scientific Reports. The correction addresses an error in the affiliation of one of the authors. The correct affiliation is listed as the Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia. The original article has been corrected. The authors of the article are Yuanyuan Liu, Jalil Manafian, Gurpreet Singh, Naief Alabed Alkader, and Kottakkaran Sooppy Nisar. [Extracted from the article]