Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior.

This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system's behavior and the extent to which it deviates from the unperturbed case.

Computation of soliton structure and analysis of chaotic behaviour in quantum deformed Sinh-Gordon model.

Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons' propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

Computational study of effect of hybrid nanoparticles on hemodynamics and thermal transfer in ruptured arteries with pathological dilation.

The intended research aims to explore the convection phenomena of a hybrid nanofluid composed of gold and silver nanoparticles. This research is novel and significant because there is a lack of existing studies on the flow behavior of hybrid nanoparticles with important physical properties of blood base fluids, especially in the case of sidewall ruptured dilated arteries. The implementation of combined nanoparticles rather than unadulterated nanoparticles is one of the most crucial elements in boosting the thermal conduction of fluids. The research methodology encompasses the utilization of advanced bio-fluid dynamics software for simulating the flow of the nanofluid. The physical context elucidates the governing equations of momentum, mass, momentum, and energy in terms of partial differential equations. The results are displayed in both tabular and graphical forms to demonstrate the numerical and graphical solutions. The effect of physical parameters on velocity distribution is illustrated through graphs. Furthermore, the study's findings are unique and original, and these computational discoveries have not been published by any researcher before. The finding implies that utilizing hybrid nanoparticles as drug carriers holds great promise in mitigating the effects of blood flow, potentially enhancing drug delivery, and minimizing its impact on the body.

The weakly non-linear waves propagation for Kelvin-Helmholtz instability in the magnetohydrodynamics flow impelled by fractional theory.

The weakly nonlinear wave propagation that occurs in the presence of magnetic fields, in which energy is concentrated in a narrow band of wave-numbers in a dispersive and dissipative fluid. The main objective of this paper is to analyze the ( 2 + 1 ) - dimensional elliptic nonlinear Schrodinger equation under the influence of three different fractional operators. The generalized fractional soliton solutions and propagation of magnetohydrodynamics fluid in sort of solition will be visualized. The Conformable, ß and M-truncated fractional operator applied to classical evolution Schrodinger equation. In order to get the analytical closed form solution, one of the generalized approach new extended direct algebraic method is utilized. The fractional nonlinear elliptic Schrodinger equation is developed in three different fractional sense. The similarity transformation technique converted the controlling fractional system to ordinary differential equations. The fractional analytical solutions such as, plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, trigonometric solution, shock solution, mixed shock singular solution, mixed singular solution, complex solitary shock solution, singular solution and shock wave solutions are obtained. The graphical 2-D and 3-D representation of the results is shown to express the propagation of fluid with the magnetic field by assuming the appropriate values of the involved parameters. The graphical performance of the obtained solution at various settings of parametric values and fractional order reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.

Optical Solitons with Beta and M-Truncated Derivatives in Nonlinear Negative-Index Materials with Bohm Potential.

In this article, we explore solitary wave structures in nonlinear negative-index materials with beta and M-truncated fractional derivatives with the existence of a Bohm potential. The consideration of Bohm potential produced quantum phase behavior in electromagnetic waves. The applied technique is the New extended algebraic method. By use of this approach, acquired solutions convey various types of new families containing dark, dark-singular, dark-bright, and singular solutions of Type 1 and 2. Moreover, the constraint conditions for the presence of the obtained solutions are a side-effect of this technique. Finally, graphical structures are depicted.