Numerical solutions and stability analysis for solitary waves of complex modified Korteweg–de Vries equation using Chebyshev pseudospectral methods

2020 ◽  
Vol 36 (6) ◽  
pp. 1662-1681
Author(s):  
Avinash K. Mittal ◽  
Lokendra K. Balyan
Keyword(s):  
Stability Analysis ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Pseudospectral Methods ◽  
De Vries ◽  
Chebyshev Pseudospectral

scholarly journals Computational and Numerical Solutions for 2+1-Dimensional Integrable Schwarz–Korteweg–de Vries Equation with Miura Transform

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Raghda A. M. Attia ◽  
S. H. Alfalqi ◽  
J. F. Alzaidi ◽  
Mostafa M. A. Khater ◽  
Dianchen Lu
Keyword(s):  
Solitary Waves ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Adomian Decomposition Method ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Tanh Method ◽  
De Vries ◽  
Parameter Values

This paper investigates the analytical, semianalytical, and numerical solutions of the 2+1–dimensional integrable Schwarz–Korteweg–de Vries (SKdV) equation. The extended simplest equation method, the sech-tanh method, the Adomian decomposition method, and cubic spline scheme are employed to obtain distinct formulas of solitary waves that are employed to calculate the initial and boundary conditions. Consequently, the numerical solutions of this model can be investigated. Moreover, their stability properties are also analyzed. The solutions obtained by means of these techniques are compared to unravel relations between them and their characteristics illustrated under the suitable choice of the parameter values.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Cnoidal Wave Trains and Solitary Waves in a Dissipation-Modified Korteweg—de Vries Equation

KdV ’95 ◽  
1995 ◽  
pp. 457-475
Author(s):  
A. Ye. Rednikov ◽  
M. G. Velarde ◽  
Yu. S. Ryazantsev ◽  
A. A. Nepomnyashchy ◽  
V. N. Kurdyumov
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Cnoidal Wave ◽  
De Vries ◽  
Wave Trains

scholarly journals New numerical solutions of fractional-order Korteweg-de Vries equation

2020 ◽  
Vol 19 ◽  
pp. 103326
Author(s):  
Mustafa Inc ◽  
Mohammad Parto-Haghighi ◽  
Mehmet Ali Akinlar ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Vries Equation ◽  
De Vries
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