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This research article examines the correctness of two new analytical methods for solving the internal solitary waves of shallow seas. To get the computational solutions to the positive (2 + 1)-dimensional Gardner–Kadomtsev–Petviashvili model, the extended simplest equation and modified Kudryashov methods are used. Numerous new traveling wave solutions in various forms are developed in order to assess the starting conditions required for the variational iteration technique, one of the most accurate semi-analytical methods. The semi-analytical solutions are used to demonstrate the precision of the solutions obtained and the analytical methods employed. The dynamical behavior of internal solitary waves in shallow waters is shown using many three-dimensional drawings. The performance of the used schemes demonstrates their efficacy and power, as well as their capacity to handle a large number of nonlinear evolution equations.

This article proposes and analyzes a fractional-order susceptible, infectious, susceptible (SIS) epidemic model with saturated treatment and disease transmission by employing four recent analytical techniques along with a novel fractional operator. This model is computationally handled by extended simplest equation method, sech–tanh expansion method, modified Khater method, and modified Kudryashov method. The results’ stable characterization is investigated through the Hamiltonian system’s properties. The analytical solutions are demonstrated through several numerical simulations.

This article investigates the dynamical and physical behavior of the second positive member in a new, utterly integrable hierarchy. This investigation depends on constructing novel analytical and approximate solutions to the Qiao model. The model’s name is after the researcher who derived the mathematical formula of it in 2007. This model possesses a Lax representation and bi-Hamiltonian structure. This study employs the unified and variational iteration (VI) method to obtain analytical and numerical solutions to the considered model. The obtained analytical solutions are used to calculate the necessary conditions for applying the suggested numerical method that makes checking the obtained solutions’ accuracy a valuable option. The obtained solutions are sketched in different techniques to explain more physical and dynamics details of the Qiao model and show the matching between obtained solutions.

Sardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrödinger’s equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.

This study explores the nonlinear Peyrard-Bishop DNA dynamic model, a nonlinear evolution equation that describes the behavior of DNA molecules by considering hydrogen bonds between base pairs and stacking interactions between adjacent base pairs. The primary objective is to derive analytical solutions to this model using the Khater III and improved Kudryashov methods. Subsequently, the stability of these solutions is analyzed through Hamiltonian system characterization. The Peyrard-Bishop model is pivotal in biophysics, offering insights into the dynamics of DNA molecules and their responses to external forces. By employing these analytical techniques and stability analysis, this research aims to enhance the understanding of DNA dynamics and its implications in fields such as drug design, gene therapy, and molecular biology. The novelty of this work lies in the application of the Khater III and an enhanced Kudryashov methods to the Peyrard-Bishop model, along with a comprehensive stability investigation using Hamiltonian system characterization, providing new perspectives on DNA molecule dynamics within the scope of nonlinear dynamics and biophysics [ABSTRACT FROM AUTHOR]

This study uses crystal lattice theory and physicochemical characterization to show a number of correct wave solutions that are like the way plasma waves move. The nonlinear time–fractional Gilson–Pickering (G P) model has been addressed using two distinct analytical and numerical techniques. This model is used in crystal lattice theory and plasma physics to show how waves move, so it is a basic model for how waves move in one direction. Utilizing the modified rational and He's variational iteration approximations in conjunction with the β–fractional derivative principles, we give the handled model fresh and precise solitary wave solutions. Various contour, three-dimensional, and two-dimensional graphs depict the determined outcomes. Compared to other recent studies, ours indicates the importance of this research area. The presented methods show how simple, direct, and effective they are and how they can be used with a wide range of nonlinear evolution equations. [ABSTRACT FROM AUTHOR]