Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

Sobolev Gradient Approach for Huxley and Fisher Models for Gene Propagation

The application of Sobolev gradient methods for finding critical points of the Huxley and Fisher models is demonstrated. A comparison is given between the Euclidean, weighted and unweighted Sobolev gradients. Results are given for the one dimensional Huxley and Fisher models.

Multiple rational rogue waves for higher dimensional nonlinear evolution equations via symbolic computation approach

The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito(HSI)equation and the newly proposed extended(3+1)-dimensional Jimbo-Miwa(JM)equation with the help of a symbolic computation technique.By incorporating a direct variable trans-formation and utilizing Hirota’s bilinear form,multiple rogue wave structures of different orders are ob-tained for both generalized HSI and JM equation.The obtained bilinear forms of the proposed equations successfully investigate the 1st,2nd and 3rd-order rogue waves.The constructed solutions are verified by inserting them into original equations.The computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue waves.Physical properties of these waves are governed by different parameters that are discussed in details.

Painlevé integrability and a collection of new wave structures related to an important model in shallow water waves

This paper investigates the perturbed Boussinesq equation that emerges in shallow water waves.The perturbed Boussinesq equation describes the properties of longitudinal waves in bars,long water waves,plasma waves,quantum mechanics,acoustic waves,nonlinear optics,and other phenomena.As a result,the governing model has significant importance in its own right.The singular manifold method and the unified methods are employed in the proposed model for extracting hyperbolic,trigonometric,and rational function solutions.These solutions may be useful in determining the underlying context of the physical incidents.It is worth noting that the executed methods are skilled and effective for examining nonlinear evaluation equations,compatible with computer algebra,and provide a wide range of wave solutions.In addition to this,the Painlevétest is also used to check the integrability of the governing model.Two-dimensional and threedimensional plots are made to illustrate the physical behavior of the newly obtained exact solutions.This makes the study of exact solutions to other nonlinear evaluation equations using the singular manifold method and unified technique prospective and deserving of further study.

Multi-solitons of Thermophoretic Motion Equation Depicting the Wrinkle Propagation in Substrate-Supported Graphene Sheets

The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.

Dipole and Combo Optical Solitons in Birefringent Fibers in the Presence of Four-Wave Mixing

The ultimate theme of this study is to develop dipole and combo optical solitons in birefringent fibers(BF) along with the effect of four-wave mixing(4 WM). Two types of rough mediums are used which are Kerr law and parabolic law. Ansatz method of Choudhuri is applied to obtain dark in the bright(dipole) soliton solutions providing bright background for the propagation of optical dark pulse. Ansatz method of Li is applied to obtain combo soliton solutions providing bright solitary wave and dark solitary wave solutions. These results also exist to hold in non-Kerr media with higher order dispersion.

Fractional soliton dynamics of electrical microtubule transmission line model with local M-derivative

In this paper,two integrating strategies namely exp[-Ф(Х)]and (G'/G^(2))-expansion methods together with the attributes of local-M derivatives have been acknowledged on the electrical microtubule(MT)model to retrieve soliton solutions.The said model performs a significant role in illustrating the waves propagation in nonlinear systems.MTs are also highly productive in signaling,cell motility,and intracellular transport.The proposed algorithms yielded solutions of bright,dark,singular,and combo fractional soliton type.The significance of the fractional parameters of the fetched results is explained and presented vividly.

Insights of numerical simulations of magnetohydrodynamic squeezing nanofluid flow through a channel with permeable walls

An analysis related to the transport of nanofluid that is confined in a channel between two orthogonal permeable walls will be investigated with the help of two numerical techniques.With the aid of the reasonable similarity changeover;the said model will be shaped into the desired non-linear equation whose behavior will be explained analytically as well as graphically where the functioning of three disparate variables such as magnetic parameter,permeable Reynold number,and channel permeable ratio will be explained precisely.The said model has been controlled by the homotopy analysis method(HAM)and then,compared through an efficient numerical method named shooting method(ShM).The profiles show that increases in the magnetic parameter decline the nanofluid flow velocity,whereas magnitude-wise raise is shown in each axial velocity profile.The radial profile raises while getting variation in wall expansion parameter from negative to positive.For the entire domain,the rate of change in velocity description enhances at the center while reduces at the surfaces.And the outcomes disclose that the wall permeable ratio has a significant impact on the solutions.Since the zero value of wall ratio refers to the particular type that Terrill has discussed.