Alyaa A. Al-Qarni

Analytical solutions for the complex-valued nonlinear Gerdjikov–Ivanov (GI) equation have been studied extensively using integrability-based methods. In contrast, numerical and semi-analytical exploration remains relatively underdeveloped. Thus, the present study deploys both the traditional Adomian decomposition method (ADM) and its improved version (IADM) to explore the computational relevance of the GI equation to shock waves against a benchmark exact soliton solution. The findings indicate that both methods are effective in addressing the GI equation, with the improved method demonstrating an enhancement in the stability of the convergence under specific conditions. This work offers the first systematic semi-analytic and numerical evaluation of the GI equation, introducing practical implementation guidelines.

This study presents a comprehensive investigation of cubic–quartic solitons within birefringent optical fibers, focusing on the effects of the Kerr law on the refractive index. The researchers have derived soliton solutions analytically using the sine-Gordon function technique. To validate their analytical results, the study employs the improved Adomian decomposition method, a numerical technique known for its efficiency and accuracy in solving nonlinear problems. This method effectively approximates solutions while minimizing computational errors, allowing for reliable numerical simulations that corroborate the analytical findings. The insights gained from this research contribute to a deeper understanding of the symmetry properties involved in nonlinear wave propagation in optical fibers. The study highlights the significant role of nonlinearities in shaping the behavior of waves within these systems. The use of proposed method not only serves as a checking mechanism for the sine-Gordon solutions but also illustrates its potential applicability to other nonlinear systems exhibiting complex symmetry behaviors. This versatility could lead to new exploration fronts in nonlinear optics and photonics, expanding the toolkit available for researchers in these rapidly evolving fields.

One of the most cutting-edge ways to combat cancerous cells is to use cell drug carriers. These microorganisms swarm affected cells, preventing them from spreading throughout the body when they come into contact with outside stimuli. This work proposes a new type of non-Newtonian fluid flow through microvessel contains oxytactic motile microorganisms beside nanoparticles. These microorganisms swim up the oxygen concentration gradient, they also are oxygen consumers. These microorganisms serve as drug carriers to attack and destroy hypoxic tumor cells. The movement of these items within a porous peristaltic conduit that a fluid supported by nanoparticles travels through is represented mathematically in this work. The mathematical model accounts for the impact of thermal radiation forces, thermophoresis force, and Brownian motion using the main governing equations describing this issue such as momentum, heat, concentration, microorganisms, and oxytactic microorganisms transportation, which are solved using the Adomian decomposition method. The findings concentrated on demonstrating the thermal and streamlined distribution behavior of the flow in the presence of microorganisms. These results were demonstrated through a series of graphs followed by analysis in detail. In summary, some important results were discovered from the physical analysis, such as an increase in effective thermal diffusivity while resisting the diffusivity of oxytactic microorganisms, which decays the microorganism’s dispersion. Furthermore, the non-Newtonian Sutterby parameter causes a temperature decrease in all conduit domains because it opposes fluid motion. This study is expected to offer further possibilities for enhancing drug-carrier applications in hypoxic tumor areas by gaining a better understanding of the blood flow characteristics in those places.

This paper inspects the combined effects of heat and mass transfers in a hybridized Williamson viscous nanofluid composed of cadmium telluride (CdTe) and silicon carbide (SiC) nanoparticles in RT42 (Rubitherm) as base fluid in the existence of heat source and thermal radiative aspects. Knowing that the base fluid RT42 is a phase change material (PCM), it is also considered that the surface on which the nanofluid flows is an expandable surface with varying thickness. The influence of chemical reactions process and viscous dissipation on the flow and temperature of the hybridized nanofluid is examined. The parameters’ influences on the problem are evaluated after setting appropriate similarity transformations to transform the collection of major partial differential equations (PDEs) into nondimensional ordinary differential equations (ODEs). The study concludes that the presence of hybridized nanoparticles of CdTe and SiC reduces the horizontal and vertical surface frictional forces of the hybrid nanofluid. The integration of nanoparticles in RT42 enhances heat transfer rates and reduces mass transfer. The thermal radiative variable declines the heat transfer of hybridized nanofluid. The results indicate that altering the variable parameter of surface thickness reduces frictional forces in both directions.

The standard pantograph delay equation (SPDDE) is one of the famous delay models. This standard model is basically homogeneous in nature and it has been extensively studied in the literature. However, the studies on the general inhomogeneous form of such a model seem rare. This paper considers the inhomogeneous pantograph delay equation (IPDDE) with a kind of arbitrary inhomogeneous term. This arbitrary inhomogeneous term is used in different forms to generate various classes of IPDDEs. The solutions of the present classes are obtained in closed series forms which satisfy the criteria of convergence. Also, the exact solutions are determined for these classes under a certain relation between the given initial condition of the model and the initial value of the inhomogeneous term. Several classes are generated and solved when the inhomogeneous term takes the form of trigonometric, exponential, and hyperbolic functions. Some existing results in the literature are recovered as special cases of the present ones. Moreover, the behaviors of the obtained solutions are demonstrated through graphs for various kinds of IPDDEs.

The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy.