scholarly journals New Periodic Solitary Wave Solutions for a Variable-Coefficient Gardner Equation from Fluid Dynamics and Plasma Physics

2010 ◽  
Vol 01 (04) ◽  
pp. 307-311 ◽  
Author(s):  
Mohamed Aly Abdou
Keyword(s):  
Fluid Dynamics ◽  
Solitary Wave ◽  
Plasma Physics ◽  
Variable Coefficient ◽  
Solitary Wave Solutions ◽  
Gardner Equation ◽  
Wave Solutions

Solitary wave solutions of (2+1)-dimensional Maccari system

2021 ◽  
pp. 2150391
Author(s):  
Ghazala Akram ◽  
Naila Sajid
Keyword(s):  
Nonlinear Optics ◽  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this article, three mathematical techniques have been operationalized to discover novel solitary wave solutions of (2+1)-dimensional Maccari system, which also known as soliton equation. This model equation is usually of applicative relevance in hydrodynamics, nonlinear optics and plasma physics. The [Formula: see text] function, the hyperbolic function and the [Formula: see text]-expansion techniques are used to obtain the novel exact solutions of the (2+1)-dimensional Maccari system (arising in nonlinear optics and in plasma physics). Many novel solutions such as periodic wave solutions by [Formula: see text] function method, singular, combined-singular and periodic solutions by hyperbolic function method, hyperbolic, rational and trigonometric solutions by [Formula: see text]-expansion method are obtained. The exact solutions are shown through 3D graphics which present the movement of the obtained solutions.

scholarly journals Abundant novel solitary wave Solutions of two-mode Sawada-Kotera model and its Applications

2021 ◽  
Author(s):  
Ammar Oad ◽  
Muhammad Arshad ◽  
Muhammad Shoaib ◽  
Dianchen Lu ◽  
Li Xiaohong
Keyword(s):  
Applied Sciences ◽  
Fluid Dynamics ◽  
Solitary Wave ◽  
Acoustic Waves ◽  
Linear Wave ◽  
Solitary Wave Solutions ◽  
Ion Acoustic Waves ◽  
Wave Solutions ◽  
Physical Phenomena ◽  
Wave Phenomena

The Sawada-Kotera equations illustrating the non-linear wave phenomena in shallow water, ion-acoustic waves in plasmas, fluid dynamics etc. In this article, the two-mode Sawada-Kotera equation (tmSKE) occurring in fluid dynamics is addresses. The improved F-expansion and generalized exp$(-\phi(\zeta))$-expansion methods are utilized in this model and abundant of solitary wave solutions of different kinds such as bright and dark solitons, multi peak soliton, breather type waves, periodic solutions and other wave results are obtained. These achieved abundant novel solitary and other wave results have significant applications in fluid dynamics, applied sciences and engineering. By granting appropriate values to parameters, the structures of few results are presented in which many structures are novel. The graphical moments of few solutions helps the engineers and scientist for understanding the physical phenomena of this model. To explain the novelty between the present results and the previously attained results, a comparative study has been carried out. Furthermore, the executed techniques can be employed for further studies to explain the realistic phenomena arising in fluid dynamics correlated with any physical and engineering problems.

Numerical soliton solutions of fractional modied (2 + 1)-dimensional Konopelchenko-Dubrovsky equations in plasma physics

2021 ◽  
Author(s):  
Santanu Saha Ray ◽  
B Sagar
Keyword(s):  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Scheme ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Kansa Method

Abstract In this paper, the time-fractional modied (2+1)-dimensional Konopelchenko-Dubrovsky equations have been solved numerically using the Kansa method, in which the multiquadrics used as radial basis function. To achieve this, a numerical scheme based on nite dierenceand Kansa method has been proposed. Also the solitary wave solutions have been obtained by using Kudryashov technique. The computed results are compared with the exact solutions as well as with the soliton solutions obtained by Kudryashov technique to show the accuracy of the proposed method.

scholarly journals The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Wei-Guo Zhang ◽  
Xing-Qian Ling ◽  
Xiang Li ◽  
Shao-Wei Li
Keyword(s):  
Solitary Wave ◽  
Numerical Simulations ◽  
Hypergeometric Function ◽  
Solitary Waves ◽  
Orbital Stability ◽  
Solitary Wave Solutions ◽  
Gaussian Hypergeometric Function ◽  
Gardner Equation ◽  
Wave Solutions ◽  
Generalized Gardner Equation

In this paper, the orbital stability of solitary wave solutions for the generalized Gardner equation is investigated. Firstly, according to the theory of orbital stability of Grillakis-Shatah-Strauss, a general conclusion is given to determine the orbital stability of solitary wave solutions. Furthermore, on the basis of the two bell-shaped solitary wave solutions of the equation, the explicit expressions of the orbital stability discriminants are deduced to give the orbitally stable and instable intervals for the two solitary waves as the wave velocity changing. Moreover, the influence caused by the interaction between two nonlinear terms is also discussed. From the conclusion, it can be seen that the influences caused by this interaction are apparently when 0<p<4, which shows the complexity of this system with two nonlinear terms. Finally, by deriving the orbital stability discriminant d′′(c) in the form of Gaussian hypergeometric function, the numerical simulations of several main conclusions are given in this paper.

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