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The variant Boussinesq equation has significant application in propagating long waves on the surface of the liquid layer under gravity action. In this article, the improved Bernoulli subequation function (IBSEF) method and the new auxiliary equation (NAE) technique are introduced to establish general solutions, some fundamental soliton solutions accessible in the literature, and some archetypal solitary wave solutions that are extracted from the broad-ranging solution to the variant Boussinesq wave equation. The established soliton solutions are knowledgeable and obtained as a combination of hyperbolic, exponential, rational, and trigonometric functions, and the physical significance of the attained solutions is speculated for the definite values of the included parameters by depicting the 3D profiles and interpreting the physical incidents. The wave profile represents different types of waves associated with the free parameters that are related to the wave number and velocity of the solutions. The obtained solutions and graphical representations visualize the dynamics of the phenomena and build up the mathematical foundation of the wave process in dissipative and dispersive media. It turns out that the IBSEF method and the NAE are powerful and might be used in further works to find novel solutions for other types of nonlinear evolution equations ascending in physical sciences and engineering.

The Korteweg-de Vries equation (KdV) and the (2+ 1)-dimensional Nizhnik-Novikov-Veselov system (NNV) are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially) integrable equations. Compared with Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.

In this paper, we introduce a numerical and analytical study of the HIV‐1 infection of CD4+ T‐cells conformable fractional mathematical model. This model is studied analytically by Kudryashov and modified Kudryashov methods and numerically by finite difference method. A comparison between the results of the analytical and numerical methods is investigated. We also give some figures that show how accurate the solutions will be obtained from analytical and numerical methods. [ABSTRACT FROM AUTHOR]

The main aim of this work is to numerically investigate a mathematical model of the HIV/AIDS disease with awareness effect, as the fractional derivatives capture more the genetic and memory properties of the biological models in comparison to the classical derivative. Therefore, in this article, we utilize the generalized Caputo fractional derivative to extend the integer‐order model of HIV/AIDS transmission to fractional order. A novel fixed‐point approach is used to identify the existence and uniqueness of the FO model. We use a new numerical technique based on the Adams‐Bashforth predictor‐corrector method to solve the fractional‐order HIV/AIDS transmission model. We illustrated the obtained numerical results through graphs. [ABSTRACT FROM AUTHOR]

In this work, the generalized Kudryashov method is used to obtain the exact traveling wave solutions for two important nonlinear evolution equations, the Chaffee–Infante equation in (2 + 1)‐dimensions and the dimensionless Zakharov equation. The generalized Kudryashov method is successfully used for getting exact solutions of these nonlinear equations in the form of exponential function solutions and hyperbolic function solutions. Moreover, we have discussed the dynamical behaviors through graphical representation of the solutions obtained in this way. [ABSTRACT FROM AUTHOR]

In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell‐Whitehead‐Segel–type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement. [ABSTRACT FROM AUTHOR]

In this article, we construct the exact dynamical wave solutions to the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative by using an efficient and well-established approach, namely: the two-variable G ' / G ,     1 / G -expansion method. The solutions of the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative play a vital role in many scientific occurrences. The regular dynamical wave solutions of the abovementioned equation imply three different fundamental functions, which are the trigonometric function, the hyperbolic function, and the rational function. These solutions are classified graphically into three categories, such as singular periodic solitary, kink soliton, and anti-kink soliton wave solutions. Furthermore, the effect of the fractional parameter on these solutions is discussed through 2D plots. [ABSTRACT FROM AUTHOR]

Purpose: To analyze the distribution of stresses for mandibular Kennedy class I removable partial overdentures submitted to different implant lengths and clasp designs., Materials and Methods: Twenty-seven heat-cured acrylic resin casts with a uniform soft acrylic layer were constructed from models representing the mandibular Kennedy class I removable partial denture with the first premolars terminal abutment on both sides. The casts were grouped into a control group, group I, and group II with three casts of each for designing a different clasp on the last abutment with Rest, Proximal plate, Aker circumferential (RPA), Rest, Proximal plate, I-bar (RPI), and wrought wire (WW). All casts were submitted to vertical load for stress analysis after preparing channels at the buccal/distal surface of abutments, the crest of the ridge, and the buccal/lingual of the implant for placement of uniaxial strain gauges that can convert the electro-signals to micro-strain by using the software. Kolmogorov-Smirnov normality test, independent t-test, and one-way anlysis of Variance (ANOVA) test followed by Tukey`s Post Hoc for multiple comparisons test were used for statistical analysis., Results: The control group results revealed more significant stresses on the ridge with RPA and RPI clasps but on the abutment with WW clasp as P < 0.05. In group I, the ridge was significantly stressed more than the implant followed by the abutment when the RPA clasp was used while there was insignificance on the implant with RPA and RPI as p > 0.05. In group II, the stresses were more on the abutment with RPA, RPI, and WW clasps followed by lower on the implant and lowest on the ridge., Conclusions: Proper implant and clasp type selection are critical for stress distribution on the ridge, abutment, and implant when using removable partial overdenture. The stresses on longer implants are tolerated and more widely distributed than shorter ones., (© 2024 by the American College of Prosthodontists.)