scholarly journals Bright–Dark Soliton Waves’ Dynamics in Pseudo Spherical Surfaces through the Nonlinear Kaup–Kupershmidt Equation

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 963
Author(s):  
Mostafa M. A. Khater ◽  
Lanre Akinyemi ◽  
Sayed K. Elagan ◽  
Mohammed A. El-Shorbagy ◽  
Suleman H. Alfalqi ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Nonlinear Optics ◽  
Plasma Physics ◽  
Analytical Solutions ◽  
Analytical Methods ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Dark Soliton ◽  
Physical Behavior ◽  
Spherical Surfaces

The soliton waves’ physical behavior on the pseudo spherical surfaces is studied through the analytical solutions of the nonlinear (1+1)–dimensional Kaup–Kupershmidt (KK) equation. This model is named after Boris Abram Kupershmidt and David J. Kaup. This model has been used in various branches such as fluid dynamics, nonlinear optics, and plasma physics. The model’s computational solutions are obtained by employing two recent analytical methods. Additionally, the solutions’ accuracy is checked by comparing the analytical and approximate solutions. The soliton waves’ characterizations are illustrated by some sketches such as polar, spherical, contour, two, and three-dimensional plots. The paper’s novelty is shown by comparing our obtained solutions with those previously published of the considered model.

Inhomogenous diffusion equations in plasma physics and fluid dynamics

1978 ◽  
Vol 56 (1) ◽  
pp. 23-29
Author(s):  
C. S. Lai
Keyword(s):  
Fluid Dynamics ◽  
Plasma Physics ◽  
Analytical Solutions ◽  
Diffusion Coefficients ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Diffusion Characteristics ◽  
Self Similar Solution ◽  
Self Similar ◽  
Inhomogeneous Diffusion

Using the method of self-similar solution of partial differential equations, analytical solutions for the two- and three-dimensional inhomogeneous diffusion equations with the diffusion coefficients D ~ rm are obtained. The solutions found can be useful in studying the diffusion characteristics of some fluids and plasmas.

Comment on ‘Study of lump solutions to an extended Calogero-Bogoyavlenskii-Schiff equation involving three fourth-order terms’ (2020 Phys. Scr. 95 095207)

2021 ◽  
Vol 96 (12) ◽  
pp. 127001
Author(s):  
Xin-Yi Gao ◽  
Yong-Jiang Guo ◽  
Wen-Rui Shan
Keyword(s):  
Fluid Dynamics ◽  
Nonlinear Optics ◽  
Plasma Physics ◽  
Symbolic Computation ◽  
Fourth Order ◽  
Analytic Solutions ◽  
Hirota Method ◽  
Bäcklund Transformations ◽  
Current Interest ◽  
Lump Solutions

Abstract Of current interest, in nonlinear optics, fluid dynamics and plasma physics, the paper commented (i.e., Phys. Scr. 95, 095207, 2020) has investigated a (2+1)-dimensional extended Calogero-Bogoyavlenskii-Schiff system. Hereby, we make the issue raised in that paper more complete. Using the Hirota method and symbolic computation, we construct three sets of the bilinear auto-Bäcklund transformations for that system, along with some analytic solutions. As for the amplitude of the relevant wave in nonlinear optics, fluid dynamics or plasma physics, our results depend on the coefficients in that system.

Photoelastic determination of stress intensity factors for single and interacting cracks and comparison with calculated results. Part II: Three-dimensional problems

1984 ◽  
Vol 19 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Y Phang ◽  
C Ruiz
Keyword(s):  
Stress Intensity ◽  
Analytical Solutions ◽  
Stress Intensity Factors ◽  
Three Dimensional ◽  
Circular Crack ◽  
Approximate Solutions ◽  
Intensity Factors ◽  
Central Crack ◽  
Exact Analytical Solutions

The application of the frozen stress photoelastic technique to the determination of stress intensity factors in two-and three-dimensional problems is discussed. The technique, involving casting flaws by the insertion of thin shims, is found to give accurate results for problems with a known exact analytical solutions: a central crack in a wide plate and an embedded circular crack. It is applied to other problems without a known solution or for which only approximate solutions, often providing inconsistent answers exist.

On Analytical Routes to Chaos in Nonlinear Systems

2014 ◽  
Vol 24 (04) ◽  
pp. 1430013 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Analytical Solutions ◽  
Analytical Methods ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
Approximate Solutions ◽  
Periodic Motions ◽  
Approximate Methods ◽  
Nonlinear Dynamical ◽  
Analytical Bifurcation Trees

In this paper, the analytical methods for approximate solutions of periodic motions to chaos in nonlinear dynamical systems are reviewed. Briefly discussed are the traditional analytical methods including the Lagrange stand form, perturbation methods, and method of averaging. A brief literature survey of approximate methods in application is completed, and the weakness of current existing approximate methods is also discussed. Based on the generalized harmonic balance, the analytical solutions of periodic motions in nonlinear dynamical systems with/without time-delay are reviewed, and the analytical solutions for period-m motion to quasi-periodic motion are discussed. The analytical bifurcation trees of period-1 motion to chaos are presented as an application.

scholarly journals Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1003-1010
Author(s):  
Asıf Yokuş ◽  
Hülya Durur ◽  
Taher A. Nofal ◽  
Hanaa Abu-Zinadah ◽  
Münevver Tuz ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Analytical Methods ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Mathematical Tool ◽  
Symbolic Calculation ◽  
Advantages And Disadvantages ◽  
Wave Solutions

Abstract In this article, the Sinh–Gordon function method and sub-equation method are used to construct traveling wave solutions of modified equal width equation. Thanks to the proposed methods, trigonometric soliton, dark soliton, and complex hyperbolic solutions of the considered equation are obtained. Common aspects, differences, advantages, and disadvantages of both analytical methods are discussed. It has been shown that the traveling wave solutions produced by both analytical methods with different base equations have different properties. 2D, 3D, and contour graphics are offered for solutions obtained by choosing appropriate values of the parameters. To evaluate the feasibility and efficacy of these techniques, a nonlinear evolution equation was investigated, and with the help of symbolic calculation, these methods have been shown to be a powerful, reliable, and effective mathematical tool for the solution of nonlinear partial differential equations.

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