Travelling wave solutions of the third-order KdV equation using Jacobi elliptic function method

Haider, Jamil Abbas; Asghar, S.; Nadeem, Sohail

doi:10.1142/s0217979223501175

Cited by 14 publications

(6 citation statements)

References 11 publications

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“…With this method, one can get a lot of travelling wave solutions with any parameters, and the wave solutions are written in terms of elliptic functions. It is shown that the new generalised Jacobi elliptic function expansion method is a powerful and clear way to solve nonlinear partial differential equations in mathematical physics and engineering [37].…”

Section: Modelmentioning

confidence: 99%

“…In mathematics, a group of fundamental elliptic functions known as the Jacobi elliptic functions can be found easily. One can find the applications of these functions in the characterisation of the oscillation of a pendulum and in the design of electronic elliptic filters [37]. Jacobi's elliptic operations are the generalisation that refers to those other conics, the ellipse in particular, whereas trigonometry functions are specified concerning a circle.…”

Section: Introductionmentioning

confidence: 99%

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Travelling Wave Solutions of the Non-Linear Wave Equations

Haider

Gul

Rahman

et al. 2023

Acta Mechanica Et Automatica

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This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. The periodic solutions are found using this method which contains both solitary wave and shock wave solutions. In this paper, the new results are computed using the closed-form solution including solitary or shock wave solutions which are obtained using Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised and the periodic behaviour of the solution is described in detail. The shock waves are found to break with time, whereas, solitary waves are found to be improved continuously with time.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Travelling Wave Solutions of the Non-Linear Wave Equations

Haider

Gul

Rahman

et al. 2023

Acta Mechanica Et Automatica

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“…The goal of the ideal homotopy equation is to minimize an objective function, which may have to do with deflection, stress, power usage, or any other relevant performance indicator. Engineers and researchers can improve the design and performance of MEMS devices by finding the ideal values for system parameters by solving the optimal homotopy equation [29][30][31][32][33][34]. Through the examination of different design configurations and optimization methodologies made possible by this methodology, the field of MEMS is ultimately advanced, and the functionality and efficiency of MEMSs in a variety of applications are improved.…”

Section: Introductionmentioning

confidence: 99%

The Homotopy Perturbation Method for Electrically Actuated Microbeams in Mems Systems Subjected to Van Der Waals Force and Multiwalled Carbon Nanotubes

Amir,

Haider,

Ashraf

2024

Acta Mechanica Et Automatica

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This paper presents a summary of a study that uses the Aboodh transformation and homotopy perturbation approach to analyze the behavior of electrically actuated microbeams in microelectromechanical systems that incorporate multiwalled carbon nanotubes and are subjected to the van der Waals force. All of the equations were transformed into linear form using the HPM approach. Electrically operated microbeams, a popular structure in MEMS, are the subject of this work. Because of their interaction with a nearby surface, these microbeams are sensitive to a variety of forces, such as the van der Waals force and body forces. MWCNTs are also incorporated into the MEMSs in this study because of their special mechanical, thermal, and electrical characteristics. The suggested method uses the HPM to model how electrically activated microbeams behave when MWCNTs and the van der Waals force are present. The nonlinear equations controlling the dynamics of the system can be roughly solved thanks to the HPM. The HPM offers a precise and effective way to analyze the microbeam’s reaction to these outside stimuli by converting the nonlinear equations into linear forms. The study’s findings shed important light on how electrically activated microbeams behave in MEMSs. A more thorough examination of the system’s performance is made possible with the addition of MWCNTs and the van der Waals force. With its ability to approximate solutions and characterize system behavior, the HPM is a potent instrument that improves comprehension of the physics at play and facilitates the design and optimization of MEMS devices. The aforementioned method’s accuracy is verified by comparing it with published data that directly aligns with Anjum et al.’s findings. We have faith in this method’s accuracy and its current application.

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“…The potential applications of peristaltic flow of nanofluids in the biomedical field, such as drug delivery systems and targeted therapy, have also generated significant interest among researchers [13][14]. The study of the peristaltic flow of nanofluids is a rapidly growing field that presents numerous opportunities for research and development, with potential applications in various areas, including energy, industrial, and biomedical sectors [15][16][17][18]. The peristaltic flow of nanofluids with heat transfer is a field of fluid mechanics that combines the study of peristaltic motion with the unique properties of nanofluids, which are colloidal suspensions containing nanoparticles dispersed in a base fluid, and heat transfer [19].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Heat Transfer and Peristaltic Flow Through a Asymmetric Channel Having Variable Viscosity and Electric Conductivity

Haider,

Gul,

Nadeem

2023

Scientia Iranica

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The peristaltic flow of nanofluids is a topic of growing interest in fluid dynamics. This study investigates the effect of temperature-dependent viscosity and electric conductivity on the peristaltic flow of nanofluids. The mathematical model of the peristaltic flow is developed using the governing equations of continuity, momentum, and energy for a Newtonian fluid. Large wavelength and small Reynolds number assumptions are used to study peristaltic flow to simplify the equations of continuity, momentum, and energy. In this article, the nanofluids are assumed to be electrically conducting and temperature dependent, and the effects of Hartman number and Eckert number is studied. The resulting equations are solved using the Shooting Method. The results show that the temperature-dependent viscosity and electric conductivity significantly affect the peristaltic flow of nanofluids. The flow rate and pressure gradient decrease with increasing viscosity and conductivity while the temperature and heat transfer rate increase. Moreover, the nanofluid concentration and particle size significantly impact the flow characteristics. In conclusion, this study comprehensively analyses the peristaltic flow of nanofluids with temperature-dependent viscosity and electric conductivity. The results can be useful for understanding the behaviour of nanofluids in various applications, such as drug delivery systems, microfluidics, and thermal management.

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Travelling wave solutions of the third-order KdV equation using Jacobi elliptic function method

Cited by 14 publications

References 11 publications

Travelling Wave Solutions of the Non-Linear Wave Equations

Travelling Wave Solutions of the Non-Linear Wave Equations

The Homotopy Perturbation Method for Electrically Actuated Microbeams in Mems Systems Subjected to Van Der Waals Force and Multiwalled Carbon Nanotubes

Numerical Investigation of the Heat Transfer and Peristaltic Flow Through a Asymmetric Channel Having Variable Viscosity and Electric Conductivity

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