New soliton solutions of kraenkel-manna-merle system with beta time derivative

Bayrakci, Ugur; Tuluce Demiray, Seyma; Yildirim, Huseyin

doi:10.1088/1402-4896/ad05af

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Revolutionary physicists like Klein strived to integrate quantum mechanics into a unified five-dimensional theory, encompassing both general relativity and electrodynamics. This pursuit aimed at establishing a comprehensive understanding that bridged the gap between quantum phenomena and the fundamental principles of relativistic physics [19][20][21]. In current study, our objective is to derive new and broadly applicable solitary wave solutions for the nonlinear KGE.…”

Section: The Governing Modelmentioning

confidence: 99%

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Construction of new wave structures and stability analysis for the nonlinear Klein-Gordon equation

Tariq,

Bekir,

Nisar

et al. 2024

Phys. Scr.

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In this study, the nonlinear Klein-Gordon equation the relativistic equivalents of the nonlinear Schrödinger equations is presented which characterizes the connection between relativistic energy-momentum in a quantized manner. A variety of exact solutions are developed by employing the extended Fan sub-equation approach and the sardar sub-equation method. The study includes three dimensionalsurface plots of some derived solutions like dark and bright solitary waves, kink solitary waves, anti-kink solitary waves, periodic solitary waves and hyperbolic functions, with several solutions being novel. Furthermore, the stability analysis of the observed solutions is also established to validate the scientific computations. The 3D, 2D and contour visualizations of the wave dynamics are demonstrated using Mathematica for a suitable choice of parameters. The applied strategies are recognized as a significant mathematical tool for obtaininganalytical solutions to partial differential equations in mathematical physics.

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Section: The Governing Modelmentioning

confidence: 99%

“…is essential to determine the values of l 0 and l 1 , while ensuring that χ satisfies the given conditions h h i (i = 0, 1, 2, 3, 4) are introduced.The analysis advances by choosing the coefficients of ζ j ζ ( k) and inserting equations equation(19) and equation (20) into equation equation(18) ( )…”

mentioning

confidence: 99%

Construction of new wave structures and stability analysis for the nonlinear Klein-Gordon equation

Tariq,

Bekir,

Nisar

et al. 2024

Phys. Scr.

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Diversity of solitonic wave structures to the M‐truncated dynamical system in ultrasound imaging

Yao,

Younas

2024

Math Methods in App Sciences

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The utilization of ultrasound imaging has become extensively prevalent and well‐established in clinical practice. The fundamental technologies that serve as the foundation for various applications in the field include transducers, beam shaping, pulse compression, tissue harmonic imaging, contrast agents, methodologies for quantifying blood flow and tissue motion, and three‐dimensional imaging. This article focuses on the examination of ultrasonic propagation, which involves the transmission of mechanical vibrations within the molecules or particles of a material. It quantifies the velocity of sound propagation in the medium of air. The third‐order nonlinear M‐fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. The recently developed computational methods have been applied in this study. The different wave structures are secured in various forms of solitary wave solutions including bright, dark, and combo solitons. In the domains of medical imaging and therapy, the investigation of sound wave propagation and high‐amplitude phenomena is facilitated by the utilization of wave structures. The effectiveness of these solutions extends to acoustic cavitation, acoustic levitation, underwater acoustics, and facilitating the process of ultrasonic propagation in tissue. Ultrasound imaging technologies currently find application in the medical field, enabling the visualization and examination of internal human tissue. This technology exhibits a wide array of applications in the fields of industry and medicine. A representation of the graphs is produced using the appropriate parametric values. The results suggest that the chosen approaches exhibit effectiveness, viability, and adaptability when implemented in complex systems in various fields, with particular emphasis on ultrasonic imaging.

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Novel soliton solution of discrete nonlinear Schrödinger system in nonlinear optical fiber

Asghari,

Eslami,

Matinfar

et al. 2024

Alexandria Engineering Journal

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New soliton solutions of kraenkel-manna-merle system with beta time derivative

Cited by 3 publications

References 28 publications

Construction of new wave structures and stability analysis for the nonlinear Klein-Gordon equation

Construction of new wave structures and stability analysis for the nonlinear Klein-Gordon equation

Diversity of solitonic wave structures to the M‐truncated dynamical system in ultrasound imaging

Novel soliton solution of discrete nonlinear Schrödinger system in nonlinear optical fiber

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