scholarly journals Stability of large- and small-amplitude solitary waves in the generalized Korteweg–de Vries and Euler–Korteweg/Boussinesq equations

2011 ◽  
Vol 251 (9) ◽  
pp. 2515-2533 ◽  
Author(s):  
J. Höwing
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Boussinesq Equations ◽  
De Vries

Boussinesq solution for solitary waves in uniform channels with sloping side walls

2000 ◽  
Vol 214 (6) ◽  
pp. 781-787 ◽  
Author(s):  
M H Teng
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Wave Speed ◽  
Side Wall ◽  
Boussinesq Equations ◽  
Wave Profile ◽  
Cross Sectional ◽  
Side Walls ◽  
Boussinesq Solution ◽  
Wall Slope

The analytical solution to the Boussinesq equations for solitary waves travelling in uniform water channels with sloping side walls is presented. Quantitative effects of channel cross-sectional geometry and channel side-wall slope at the waterline on the wave profile and wave speed, as well as the criteria for positive solitary waves to exist, are discussed. The new Boussinesq solution is also compared with the existing Korteweg-de Vries solution obtained by Peregrine. It is found that the two solutions are consistent for small amplitude waves while, for relatively large waves, the Boussinesq solution gives different predictions for wave speed and for the criteria for solitary waves to exist.

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.

scholarly journals Numerical Modeling of the Interaction of Solitary Waves and Submerged Breakwaters with Sharp Vertical Edges Using One-Dimensional Beji & Nadaoka Extended Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohammad H. Jabbari ◽  
Parviz Ghadimi ◽  
Ali Masoudi ◽  
Mohammad R. Baradaran
Keyword(s):  
Solitary Waves ◽  
Numerical Study ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Linear Interpolation ◽  
Reflected Waves ◽  
One Dimensional ◽  
Propagating Waves ◽  
Linear Elements ◽  
Predictor Corrector

Using one-dimensional Beji & Nadaoka extended Boussinesq equation, a numerical study of solitary waves over submerged breakwaters has been conducted. Two different obstacles of rectangular as well as circular geometries over the seabed inside a channel have been considered in view of solitary waves passing by. Since these bars possess sharp vertical edges, they cannot directly be modeled by Boussinesq equations. Thus, sharply sloped lines over a short span have replaced the vertical sides, and the interactions of waves including reflection, transmission, and dispersion over the seabed with circular and rectangular shapes during the propagation have been investigated. In this numerical simulation, finite element scheme has been used for spatial discretization. Linear elements along with linear interpolation functions have been utilized for velocity components and the water surface elevation. For time integration, a fourth-order Adams-Bashforth-Moulton predictor-corrector method has been applied. Results indicate that neglecting the vertical edges and ignoring the vortex shedding would have minimal effect on the propagating waves and reflected waves with weak nonlinearity.

Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma

2013 ◽  
Vol 20 (1) ◽  
pp. 012113 ◽  
Author(s):  
Manjistha Dutta ◽  
Samiran Ghosh ◽  
Rajkumar Roychoudhury ◽  
Manoranjan Khan ◽  
Nikhil Chakrabarti
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Magnetized Plasma ◽  
Electron Acoustic

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
Sign in / Sign up

Export Citation Format

Share Document