Analysis of bifurcation, chaotic structures, lump and $ M-W $-shape soliton solutions to $ (2+1) $ complex modified Korteweg-de-Vries system

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(6), P. 16116 - 16145

Published: Jan. 1, 2024

<abstract><p>This research focuses on the fascinating exploration of $ (2+1) $-dimensional complex modified Korteweg-de Vries (CmKdV) system, exhibiting its dynamics and solitary wave solutions. This system is a versatile mathematical model that finds applications in various branches physics, including fluid dynamics, plasma optics, nonlinear dynamics. Two newly developed methodologies, namely auxiliary equation (AE) method Hirota bilinear (HB) method, are implemented for construction novel solitons formats. Numerous soliton solutions synthesised distinct formats, such as dark, bright, singular, periodic, combo, W $-shape, mixed trigonometric, exponential, hyperbolic, rational, based proposed methods. Furthermore, we also find some lump solutions, periodic cross rational wave, homoclinic breather solution, M $-shaped interaction with one kink multiwave which not documented literature. In addition, employ Galilean transformation to derive dynamic framework presented equation. Our inquiry includes wide range topics, bifurcations, chaotic flows, other intriguing properties. Also, physical demonstration acquired 3D, 2D, contour plots provided. The resulting structure results can enrich dynamical behaviors given may be useful many domains, physics well demonstrate approaches used effective worthy validation.</p></abstract>

Language: Английский

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Comparative study of blood sugar–insulin model using fractional derivatives

Journal of Taibah University for Science, Journal Year: 2024, Volume and Issue: 18(1)

Published: April 10, 2024

Many years have passed since the model that outlined connection between sugar and insulin was developed, a great deal of study investigation has subsequently been done on it. In this work, we investigated disparities in Modified Bergman's glucose–insulin Yang–Abdel–Cattani derivative Caputo–Fabrizio derivative. With our improvements, prior now includes diet, which is crucial component blood glucose model. Based results, new outperforms previous one terms accuracy. To highlight significance fractional derivatives, also established models. addition, verified existence uniqueness results offered graphical numerical depiction findings.

Language: Английский

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Analysis of Infection and Diffusion Coefficient in an SIR Model by Using Generalized Fractional Derivative

Fractal and Fractional, Journal Year: 2024, Volume and Issue: 8(9), P. 537 - 537

Published: Sept. 15, 2024

In this article, a diffusion component in an SIR model is introduced, and its impact analyzed using fractional calculus. We have included the model. order to illustrate variations. Here, we applied general derivative analyze impact. The Laplace decomposition technique employed obtain numerical outcomes of observe effect model, graphical solutions are also displayed.

Language: Английский

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Study of bifurcations, chaotic structures with sensitivity analysis and novel soliton solutions of non-linear dynamical model

Journal of Taibah University for Science, Journal Year: 2024, Volume and Issue: 18(1)

Published: Sept. 26, 2024

Language: Английский

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Turbulence of lump, stripe, and soliton waves in Saturn's magnetosphere plasmas

Physics of Fluids, Journal Year: 2025, Volume and Issue: 37(2)

Published: Feb. 1, 2025

The Zakharov–Kuznetsov equation, along with its modified forms [the and further equations], is important modeling equations for interpreting different magnetoacoustic waves in plasma. In this study, we established stable broad-ranging soliton solutions, including well-known lump- stripe-shaped obtained using the Hirota bilinear (HB) method. figures text show effect of physical parameters plasma system—dispersion turbulent dispersion coefficients—on wave height. Wave heights remain determinable values free associated them. A three-dimensional (3D) plot ascertained solutions clarified stability points studied based on bifurcation theory. results each equation make a significant contribution to analysis dust-ion-acoustic Saturn's magnetosphere. We assert that HB method reliable, appropriate, easy use, powerful extracting closed-form solutions.

Language: Английский

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Effect of trapping of electrons and positrons on the evolution of shock wave in magnetized plasma: A complex trapped K-dV burgers’ equation

Results in Physics, Journal Year: 2024, Volume and Issue: 59, P. 107617 - 107617

Published: March 26, 2024

Our research demonstrates that positive and negative ions, along with trapped electrons positrons, propagate as small-amplitude electrostatic shock waves in a magnetized collisions-less plasma. The Korteweg-de Vries Burger's (T-KdVB) equation was derived by the widely recognized standard reductive perturbation technique (RPT), employing two separate scales of coordinates. study examines impact temperature ratio on wave characteristics well positrons electrons. analysis discussion focus impacts ion number densities, densities positrons. T-KdVB equations are responsible for governing rarefactive waves. Additionally, it is important to acknowledge nonlinearity dissipation play key role controlling amplitude shock.

Language: Английский

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Computational analysis of fractional kinetic equations having Bessel–Maitland function

International Journal of Mathematics for Industry, Journal Year: 2024, Volume and Issue: unknown

Published: March 22, 2024

This paper’s objective is to arrange fractional active conditions while taking into account the Bessel–Maitland capability reported by Khan et al. The solution’s final form expressed in terms of Wright hypergeometric function, which allows us define numerous additional kinetic equation solutions. Generally, condition applied many problems astronomy and material science.

Language: Английский

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On some new travelling wave solutions and dynamical properties of the generalized Zakharov system

PLoS ONE, Journal Year: 2024, Volume and Issue: 19(10), P. e0306319 - e0306319

Published: Oct. 7, 2024

This study examines the extended version of Zakharov system characterizing dispersive and ion acoustic wave propagation in plasma. The genuine, non-dispersive field depicts a shift plasma density from its equilibrium state, whereas complex, fluctuating envelope highly oscillatory electricity. main focus analysis is on employing expanded Fan sub-equation approach to achieve some novel travelling structures including explicit, periodic, linked wave, other new exact solutions are developed for different values this parameter. Three dimensional graphs utilised examine properties obtained solutions. Furthermore, ideas planar dynamical theory applied work analyse intricate behaviour analysed model. Sensitivity analysis, multistability, quasi-periodic chaotic patterns, Poincaré map, Lyapunov characteristic exponent used features.

Language: Английский

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Effect of ion anisotropy pressure in viscous plasmas: evolution of shock wave

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: 112(19), P. 17403 - 17416

Published: July 17, 2024

Language: Английский

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