Global Impact Journal: Physics Research & Applications

Forced variable-coefficient Kawahara equations: closed-form traveling waves via tanh–coth and elliptic ansätze

2026-08-29T06:39:56+00:00

We investigated a forced variable-coefficient Kawahara equation as a nonautonomous extension of a classical fifth-order dispersive model arising in nonlinear wave propagation. Such equations are relevant in physical situations where the effective nonlinearity, dispersive balance, and external input vary with time, thereby generating wave dynamics that are not captured by the standard autonomous Kawahara equation. The main objective of this work was to derive explicit traveling-wave solutions and to clarify how temporal modulation and forcing affect the amplitude, baseline, phase, and propagation of the resulting wave structures. By introducing a traveling-wave variable with time-dependent phase together with a forcing primitive, the governing equation was reduced to ordinary differential equations amenable to exact symbolic analysis. Two complementary exact-solution procedures were then developed. First, an improved tanh–coth method based on a Riccati auxiliary equation was used to construct localized real-valued traveling-wave families. Second, an elliptic ansatz in terms of the Weierstrass ℘-function was employed to generate periodic solutions together with their solitary-wave degenerations. The obtained formulas yield explicit exact solutions and recover classical constant-coefficient Kawahara profiles as limiting cases. In addition, representative examples were examined using analytical formulas, numerical tables, and graphical diagnostics to illustrate the qualitative distinction between oscillatory forcing, decaying forcing, and the autonomous unforced regime. The results provide analytical benchmarks for forced dispersive models with time-dependent coefficients and establish a unified exact-solution framework for a broad class of non-autonomous Kawahara-type equations.

Geometry of generated quasi-ruled surfaces from their quasi-parallel curves according to the q-frame in ℝ3

2026-08-29T06:15:24+00:00

Parallel curves have been used extensively in a variety of fields during the last decade, including architecture, computer graphics, aerospace, and medicine. Despite these applications, the theoretical development of parallel curves in differential geometry has been relatively limited. In this study, we investigate parallel curves using the q-frame in three-dimensional Euclidean space, rather than the traditional Frenet frame. We introduce the new expression “quasiparallel curves” as a generalization of classical parallel curves. We also examine several geometric properties of these curves and provide rigorous proofs. In differential geometry, ruled surfaces are of great importance. They are defined by the movement of generators, which generate straight lines on the surface. Furthermore, a directrix (base curve) is any curve that intersects all generators (rulings). In this paper, we investigate a new class of quasi-ruled surfaces whose base curve is both the original curve and its quasi-parallel curve in ℝ³. We describe the geometric characteristics of these surfaces and derive the first and second fundamental forms, as well as the Gaussian and mean curvatures. Specific types of quasi-ruled surfaces are analyzed, and conditions for their developability and minimality are established. Several quasi-ruled surfaces generated from the helix curve as a base curve and others generated from its quasi-parallel curve as a base curve are provided, and the parametrization of the resulting surfaces are determined. Finally, all generated surfaces, together with their quasi-parallel and original curves, are visualized using Mathematica 13.

Structured beam generation and optical trapping of low-index particles using a semi-nonlinear Michelson interferometer

2026-08-29T06:49:03+00:00

In this work, we propose a semi-nonlinear Michelson interferometer (SNMI) for controllable laser beam shaping and optical manipulation. By placing a Kerrtype nonlinear medium into one arm of the interferometer, the phase difference between the two arms becomes intensity-dependent, enabling dynamic control of the spatial profile of the output beam through the input laser power. Numerical simulations show that a conventional Gaussian beam can be transformed into a variety of structured beams, including flat-top, ring, bottle, and hollow Gaussian beams, under appropriate operating conditions. The generated hollow beam is proposed to trap “low-index” nanoparticles, whose refractive index is lower than that of the surrounding medium. The transverse optical gradient force acting on dielectric nanoparticles is analyzed under the Rayleigh scattering regime. The results indicate that the generated hollow-type beams can produce stable trapping regions for low-index nanoparticles, which are typically difficult to trap with standard Gaussian beams. The proposed SNMI provides a simple, tunable, and flexible platform for structured beam generation, with potential applications in trapping nanoparticles, as numerically observed and discussed.

Strain wave structure of electron and positron

2026-08-29T06:26:38+00:00

By treating physical space as an elastic continuum, we show that elementary particles and their fields can be represented by stress–strain wave packets in the elastic space continuum. Dynamic equilibrium equations of elasticity reduce to vector wave equations involving displacement vectors in this continuum. We derive the equivalence between displacement vector U and the magnetic vector potential A to show that electromagnetic fields are manifestations of stress–strain fields in this continuum. The structure of the electron is modeled on a spherically symmetrical strain wave solution of the vector wave equilibrium equation. The solution consists of a central standing strain wave core approximately 2 fm in radius, surrounded by a radially decaying field of phase waves propagating outward for the positron and inwards for the electron. Approximately 37.3% of the energy of the electron is contained in its wave field and the remaining in the central standing wave core. We also derive the Coulomb interaction between two electrons and verify Coulomb’s law of electrostatics. The intrinsic electrostatic field, intrinsic spin, and magnetic field effects of the electron are derived from its strain wave structure. We also verify the Biot–Savart law for motion-induced magnetic fields and indicate the origin of De Broglie matter waves.

Analysis of thermophoretic and brownian motion effects on Newtonian and Non-Newtonian fluid flow through a porous stretching surface

2026-05-11T09:47:21+00:00

The present work explores the intricate thermo-fluid dynamics of Newtonian and non-Newtonian nanofluids flowing over a porous, deformable stretching surface. The analysis incorporates the combined influences of thermal radiation, thermophoretic force, Brownian motion, and dual-phase-lag models of heat and mass diffusion. Darcy–Forchheimer drag and slip boundary effects are also considered to represent realistic flow resistance within porous media. Through similarity transformations, the governing nonlinear partial differential equations are reduced to ordinary differential form and numerically solved using MATLAB’s bvp4c algorithm. The study reveals that enhanced permeability and slip parameters attenuate fluid motion, whereas intensified Brownian motion and porous resistance elevate the thermal boundary layer. The findings confirm that nanofluids offer superior heat transport capabilities, making them promising candidates for applications in thermal regulation and biomedical heat exchange systems. Model validation against previously published results demonstrates strong agreement, reinforcing the reliability of the numerical approach.