scholarly journals Collective coordinate framework to study solitary waves in stochastically perturbed Korteweg–de Vries equations

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Madeleine Cartwright ◽  
Georg A. Gottwald
Keyword(s):  
Solitary Waves ◽  
De Vries ◽  
Collective Coordinate ◽  
Stochastically Perturbed

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.

THE SECOND-ORDER KdV EQUATION AND ITS SOLITON-LIKE SOLUTION

2009 ◽  
Vol 23 (14) ◽  
pp. 1771-1780 ◽  
Author(s):  
CHUN-TE LEE ◽  
JINN-LIANG LIU ◽  
CHUN-CHE LEE ◽  
YAW-HONG KANG
Keyword(s):  
Solitary Waves ◽  
Soliton Solution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order ◽  
Close Resemblance ◽  
De Vries

This paper presents both the theoretical and numerical explanations for the existence of a two-soliton solution for a second-order Korteweg-de Vries (KdV) equation. Our results show that there exists "quasi-soliton" solutions for the equation in which solitary waves almost retain their identities in a suitable physical regime after they interact, and bear a close resemblance to the pure KdV solitons.

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

Pulsatile Flows

2019 ◽  
pp. 69-84
Author(s):  
Troy Shinbrot
Keyword(s):  
Solitary Waves ◽  
Mode Coupling ◽  
Bessel Functions ◽  
Kdv Equation ◽  
Nonlinear Effects ◽  
De Vries ◽  
Intrinsic Nonlinearity ◽  
Pulsatile Flows

Flow solutions in the presence of pulsation (e.g. from the heart) are developed. Bessel functions are introduced as an aside. The concepts of shocks and solitary waves (solitons) are then discussed as examples of nonlinear effects. The strategy for dealing with intrinsic nonlinearity is described in terms of mode coupling and the Korteweg–de Vries (KdV) equation.

Cylindrical and Spherical Dust-Ion Acoustic Solitary Waves by Damped Korteweg-de Vries-Burgers Equation

2019 ◽  
Vol 49 (5) ◽  
pp. 693-697 ◽  
Author(s):  
Dong-Ning Gao ◽  
Zheng-Rong Zhang ◽  
Jian-Peng Wu ◽  
Dan Luo ◽  
Wen-Shan Duan ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Burgers Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
De Vries

Dynamic Response of SPAR in Internal Solitary Waves

2011 ◽  
Author(s):  
Yan Qu ◽  
Zhijun Song ◽  
Bin Teng ◽  
Yunxiang You
Keyword(s):  
Dynamic Response ◽  
Solitary Waves ◽  
Mkdv Equation ◽  
Internal Solitary Waves ◽  
Response Analysis ◽  
Potential Hazard ◽  
Current Profile ◽  
Floating Structures ◽  
Dynamic Motion ◽  
De Vries

Internal solitary wave is considered as a potential hazard environmental condition to the floating structures in South China Sea. This paper presents results of the dynamic response analysis of a SPAR in internal solitary waves (ISW). Mathematical model of the ISW is selected to simulate the current process induced by the ISW. The result shows that the Korteweg–de Vries (KdV) gives rational result compared with the Modified Korteweg–de Vries (MKdV) equation. Dynamic motion of SPAR were estimated by using the current profile derived from KDV theory, load determined by Morrison equation and the nonlinear model of the mooring system.

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.

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