Volume 80, Issue 7

We show the canonical quantization of dynamical systems using gauge transformation. The modulating external forcing is given a structural similarity to a vector potential in the transformed effective Hamiltonian, which is similar to that of a static system. Quantization of the coupled modulation provides Lie algebra and Hilbert space spanned by eigenstates |n⟩, which we explain as external modulation generated effective quantized electromagnetic field.

The soliton solutions of the two-dimensional homogeneous Bose–Einstein Condensates Model that is related to the atomic interactions strength and the initial momentum have been discussed through this article to explain the vision when the initial momentum is sufficiently high; the thickness of the bubble-shaped BEC undergoes a counterintuitive thinning. In quantum statistics, the suggested model indicates to two available ways in which a group of noninteracting similar particles may occupy a collection of obtainable possible discrete energy states at thermodynamic equilibrium has been investigated. Many new types of soliton solutions that weren’t achieved before can be constructed, and its descriptions have been documented in the conclusion. In order to derive these new soliton perceptions of the perturbed dynamics of rotating as well as the norm square of the obtaining solution that physically denote to the envelop of these dynamics, we will apply five various schemas. The five distinct schemas that are implemented for the first time to this target are the generalized Kudryashov Schema, the Paul-Painleve Approach schema, the (G′/G)-Expansion Schema, the Extended Simple Equation Schema, and the Riccati–Bernoulli Sub Order Schema are implemented individually, independently in consecutive stages. The consistency for all explored analytical solutions are cleared although these schemas have different tools in prepared. The 2-kind and 3-kind graphs simulations as well as the norm square, which denote physically to envelop of these dynamics, have been documented. The configurator figures that detect the Dynamics’s behaviors as well as all mathematical treatment have been defined via Mathematica program.

This study aims to investigate the impact of couple stresses on the convective stability of a rotating Navier–Stokes–Voigt fluid saturating a porous medium, considering various combinations of boundary conditions. Both nonlinear and linear analyses were performed using the energy method and the normal mode analysis method, respectively. The eigenvalue problems formulated from both analyses were solved using the single-term Galerkin method to calculate the Rayleigh number. The Rayleigh numbers for nonlinear analysis and stationary convection are identical, confirming the absence of a subcritical region, ensuring global stability. The results obtained for free-free boundary conditions, in the absence of couple stresses and rotation, align with those found in Straughan’s work. The study explores the influence of key parameters such as the Kelvin–Voigt parameter, couple stress parameter, Taylor number, and Darcy–Brinkman number on the stability of the system. The results indicate that increasing the couple stresses and permeability of the medium suppresses small convection patterns, reducing the range of permissible wave numbers for oscillatory convection. Conversely, enhanced rotation and viscoelastic effects allow a broader range of wave numbers to support oscillatory convection, thereby preventing pattern merging. Couple stresses and rotational effects contribute to the stabilization of the system, while medium permeability acts as a destabilizing factor. These findings can be applied to optimize fluid dynamics and thermal management in porous media systems across diverse fields, including geophysics, engineering, petroleum recovery, and biomedical applications.

Coherent Rossby waves are integral to large-scale atmospheric processes, influencing weather patterns, energy redistribution, and global circulation. This study explores the nonlinear dynamics of these waves by deriving the two-dimensional Nonlinear Schrödinger Equation (2D-NLSE) from the 2D-Charney–Obukhov equation, which describes large-scale motion in a rotating, stratified fluid. The 2D-NLSE emerges as a powerful tool for understanding how weak nonlinearity and dispersion govern the evolution of Rossby wave packets. The 2D-NLSE reveals the influence of nonlinear interactions in shaping Rossby wave evolution, including phenomena such as wave amplitude modulation, soliton formation, and the emergence of localized structures. These nonlinear effects are pivotal for understanding the mechanisms of energy exchange across different scales in atmospheric systems. The analysis reveals that Rossby waves can give rise to the formation of rogue waves, as well as bright and kink-type Rossby wave envelope solitons. The results may contribute to the theoretical understanding of nonlinear wave propagation in geophysical systems and offer a foundation for improving predictive models for atmospheric behavior.

Nowadays graphene is emerging as one of the most exciting nanomaterial due to its continuous 29 electrically conducting behavior even at zero carrier concentration. With this initiative, we investigate the flow of magnetohydrodynamic (MHD) water, water-30%EG, water-50%EG based graphene nanofluid over a stretching surface with Thermal convection, velocity slips, and zero mass flux conditions containing gyrotactic microorganisms and nanoparticles. Thermal radiation and Arrhenius activation energy have also be under consideration. The governing fluid equations are solved by Homotopy analysis method (HAM) and computed numerically with shooting technique after employing appropriate transformations. The consequence of numerous physical parameters of velocity, concentration, temperature, and density of motile microorganism’s graphs as well as table is used for ethylene glycol based and water-based graphene nanoparticles. Additionally, perform an attentive numerical analysis of the local skin friction, Sherwood number, Nusselt number, and motile microorganisms’ density. It is observed that the improvement of the nonlinear convection variable due to temperature and heat generation variable improves the wall friction. It is found that the fluid velocity decreases as the magnetic field increases, conversely, the concentration and temperature of the fluid increases. Where the first and third-order slip parameters decrease the velocity of fluid, while the second-order slip parameter increases the velocity of fluid. Moreover, increasing the reaction rate parameters, the concentration of nanoparticle decreases, while a slight increase in E was observed with an increasing activation energy parameter. It is also found that raising the nanoparticle’s volume fraction efficiently boosts the thermal conductivity of water-50%EG when equated with water-30%EG and water nanofluids. Water-based nanofluids take more time to process as compared to ethylene glycol-based graphene nanofluids.

To investigate the effects of head-on collision (such as collision processes, phase shifts due to head-on collisions of ion-acoustic waves) and the formation of ion-acoustic (IA) KdV solitons, rogue waves (RWs), AB and KM solitons structures, an unmagnetized collisionless dusty plasma system comprising immobile (negatively charged) dust, positive and negative ions (adiabatic), and the combined Kappa–Cairns (CKC) distributed electrons in the space environment (such as H + , O 2 − and H + , H − $\left({\mathrm{H}}^{+},{\mathrm{O}}_{2}^{-}\right) \text{and} \left({\mathrm{H}}^{+},{\mathrm{H}}^{-}\right)$ plasma that existed in the D- and F-regions of the Earth’s ionosphere) and in the laboratory experiment (such as A r + , F − $\left(\mathrm{A}{\mathrm{r}}^{+},{\mathrm{F}}^{-}\right)$ plasma), is considered. The extended Poincaré–Lighthill–Kuo (ePLK) method is employed to derive the two-sided Korteweg de Vries (KdV) equations and corresponding phase shifts. The nonlinear Schrödinger equation (NLSE) is derived employing the derivative expansion method from the modified KdV (mKdV) equation. It is found that the concerned plasma parameters play a crucial role in forming the soliton structures, phase shifts, and the interaction processes of KdV solitons. The outcomes of this study will be useful to understand the collisional procedure, phase shifts, and the configurations of ion-acoustic KdV solitons, RWs, AB soliton, and KM soliton in the aforementioned environments where the relevant plasma species are identified.