Volume 79, Issue 7

In this article, the modified Kudryashov and extended simple equation methods are employed to obtain analytical solutions for the Zhiber–Shabat problem. The outcomes of this study clearly indicate that the provided methodologies are appropriate techniques for generating some new exact solutions for nonlinear evolution equations. Furthermore, the nature of the solutions would be presented in three dimensions for various parameters applying the most advanced scientific instruments. The physical behavior of the solutions are graphically displayed, and it is established that the acquired solutions are newly constructed in the form of bright, dark, optical, singular, and bell-shaped periodic soliton wave structures. The properties of the nonlinear model have been illustrated using 3D, 2D, and contour plots by selecting an appropriate set of parameters, which is demonstrated to visualize the physical structures more productively. Finally, it is concluded that similar strategies can also be implemented to study many contemporary models. To the best of our knowledge, the current work presents a novel case study that has not been previously studied in order to generate several new solutions to the governing model appearing in diverse disciplines. The results show that the strategies that have been employed are more effective and capable than the traditional methods found in previous research.

What the motivation of this paper is to provide chirped optical solitons for the complex Ginzburg–Landau equation with Hamiltonian perturbations and Kerr law nonlinearity. We get 19 exact chirped solutions by utilizing trial equation method and the complete discriminant system for polynomial method, which are richer than the solutions acquired in existing papers. We draw the two-dimensional graphs of amplitudes and corresponding chirps in order to verify the existence of the solutions and discuss the dynamical properties of the solutions. To our knowledge, this is the first time that comprehensive set of exact chirped solutions of the governing equation in the paper are obtained. The model and the results obtained in this paper may help explain some nonlinear problems.

Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.

This work presents nonlinear and linear analyses of the rotating Navier–Stokes–Voigt fluid layer that is simultaneously heated and soluted from below, considering different boundary surfaces. The energy method is used to form the eigenvalue problem for nonlinear analysis, whereas the normal mode analysis is used for the linear analysis. The Rayleigh number is numerically calculated by employing the Galerkin technique. Both nonlinear and linear analyses yield the same Rayleigh number, indicating the absence of subcritical regions and implying global stability. The Kelvin–Voigt parameter doesn’t affect the Rayleigh number for stationary convection. However, the crucial role of this parameter is established through an energy argument. The presence of rotation, Kelvin–Voigt parameter, and solute gradient give rise to oscillatory modes. Also, the effects of rotation and solute gradient are stabilizing on the system, whereas the stabilizing effect of the Kelvin–Voigt parameter becomes evident when convection exhibits an oscillatory behavior.

The electrothermoconvection in a rotating dielectric fluid layer heated from below (or above) is studied analytically using linear stability theory. First, we derive the necessary conditions for oscillatory motion when the fluid layer is heated from below and from above. Then as a consequence, sufficient conditions for the validity of the exchange principle are derived for the two configurations in terms of the parameters of the systems alone. The results hold for free boundaries for all wave numbers and for rigid boundaries with some restrictions. Further, the results for electrothermoconvection without rotation, rotatory Rayleigh–Bénard convection and Rayleigh–Bénard convection are also obtained as special cases which validate the existing results. To the best of author’s knowledge such results are not reported in the literature as far as the domain of electrothermoconvection studies is concerned.

Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” Nonlinear Dynam. , vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.

The electrospinning process allows the production of nanofibers from polymer solutions, making them suitable for various applications such as sensors, electronic devices, conductive materials, and advanced composites for high-temperature environments. In this research, polyaniline (PANI) was doped with camphor sulfonic camphor sulfonic acid (HCSA). HCSA dopant is used to modify the electrical and structural properties of polyaniline. To introduce reduced graphene oxide as a nanofiller to enhance the electrical properties of the polymer. Both the HCSA-doped PANI and HCSA-doped PANI with rGO nanofibers were electro-spun separately to create individual nanofibers. Fourier-transform infrared spectroscopy was used to investigate the chemical composition and functional groups present in the nanofibers. Field emission scanning electron microscopy was employed to study the nanofibers’ morphology, structure, and surface characteristics. Thermogravimetric analysis was used to assess the thermal stability of the nanofibers and to approximate the content of rGO. These results indicate that the addition of reduced graphene oxide (rGO) led to improvements in the nanofibers’ electrical conductivity and thermal stability.

In this work, a general eigenvalue solution of an arbitrarily constrained nonlocal strain gradient nanobeam made of functionally graded material is presented for the first time for the stability response by the effect of the Winkler foundation. Elastic springs at the ends of the nanobeam are considered in the formulation, which have not been considered in most studies. In order to analyze deformable boundary conditions, linear equation systems are derived in terms of infinite power series by using the Fourier sine series together with the Stokes’ transform. The higher-order force boundary conditions are used to obtain a coefficient matrix including different end conditions, power-law index, elastic medium, and small-scale parameters. A general eigenvalue problem of technical interest, associated with nonlocal strain gradient theory, is mathematically evaluated and presented in detail. Parametric results are obtained to investigate the effects of material length scale parameter, Winkler stiffness, power-law index, nonlocal parameter, and elastic springs at the ends. In addition, the effects of the other higher-order elasticity theories simplified from nonlocal strain gradient theory are also investigated and some benchmark results are presented.