Three-dimensional modified Korteweg-de Vries equation in a magnetised relativistic plasma with positron beam and vortex-like electron distribution

2020 ◽  
Vol 74 (2) ◽  
Author(s):  
Ridip Sarma ◽  
Apul N. Dev ◽  
Birbaishri Boro ◽  
Ranjan Das ◽  
Nirab C. Adhikary
Keyword(s):  
Electron Distribution ◽  
Vries Equation ◽  
Three Dimensional ◽  
Positron Beam ◽  
Relativistic Plasma ◽  
De Vries

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.

Three dimensional Lifshitz black hole and the Korteweg–de Vries equation

2012 ◽  
Vol 709 (3) ◽  
pp. 276-279 ◽  
Author(s):  
E. Abdalla ◽  
Jeferson de Oliveira ◽  
A. Lima-Santos ◽  
A.B. Pavan
Keyword(s):  
Black Hole ◽  
Vries Equation ◽  
Three Dimensional ◽  
De Vries ◽  
Lifshitz Black Hole

scholarly journals Rogue waves on the general periodic travelling waves background for an extended modified Korteweg-de Vries equation

2021 ◽  
Author(s):  
Yi Zhang ◽  
Yu Lou ◽  
RS Ye
Keyword(s):  
Vries Equation ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Travelling Wave ◽  
Periodic Waves ◽  
Travelling Wave Solutions ◽  
Third Order ◽  
Periodic Travelling Wave ◽  
De Vries

Under consideration in this paper is rogue waves on the general periodic travelling waves background of an integrable extended modified Korteweg-de Vries equation. The general periodic travelling wave solutions are presented in terms of the sub-equation method. By means of the Darboux transformation and the nonlinearization of the Lax pair, we present the first-, second- and third-order rogue waves on the general periodic travelling waves background. Furthermore, the dynamic behaviors of rogue periodic waves are elucidated from the viewpoint of three-dimensional structures.

The effect of the ion temperature on the ion acoustic solitary waves in a collisionless relativistic plasma

1987 ◽  
Vol 37 (3) ◽  
pp. 487-495 ◽  
Author(s):  
Yasunori Nejoh
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Relativistic Effect ◽  
Vries Equation ◽  
Oscillatory Solution ◽  
Relativistic Plasma ◽  
Ion Temperature ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
De Vries

The effect of the ion temperature on ion acoustic solitary waves in a collisionless relativistic plasma is discussed using the Korteweg–de Vries equation. The phase velocity of the ion acoustic waves decreases as the relativistic effect increases, and increases as the ion temperature increases. Only a compressional soliton of the ion acoustic wave is formed in this system. Since its amplitude increases for the lower ion temperature as the relativistic effect increases, we deduce the formation of a precursor by the presence of the streaming ions. In contrast, for the higher ion temperature, the amplitude decreases slowly. Furthermore, it is shown that the oscillatory solution of the Korteweg–de Vries equation smoothly links with the nonlinear Schrödinger equation in a relativistic plasma.

scholarly journals Three-dimensional Korteweg-de Vries equation and traveling wave solutions

2000 ◽  
Vol 24 (6) ◽  
pp. 379-384 ◽  
Author(s):  
Kenneth L. Jones
Keyword(s):  
Vries Equation ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Summation Formula ◽  
Cnoidal Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Infinite Sums ◽  
Poisson’S Summation Formula

The three-dimensional power Korteweg-de Vries equation[ut+unux+uxxx]x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integernand cnoidal wave solutions forn=1andn=2are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.

A modified Korteweg-de Vries equation for ion acoustic wavess due to resonant electrons

1973 ◽  
Vol 9 (3) ◽  
pp. 377-387 ◽  
Author(s):  
Hans Schamel
Keyword(s):  
Equation Of State ◽  
Asymptotic Behaviour ◽  
Acoustic Waves ◽  
Electron Distribution ◽  
Vries Equation ◽  
Distribution Functions ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
De Vries

The dependence of the asymptotic behaviour of small ion-acoustic waves on the number of resonant electrons is investigated by assuming an electron equation of state corresponding to the observed flat-topped electron distribution functions. The result is a modified Korteweg-de Vries equation with a stronger nonlinearity.

Integration of the nonlinear modified Korteweg-de Vries equation with a loaded term

2020 ◽  
Vol 2020 (2) ◽  
pp. 85-98
Author(s):  
A.B. Khasanov ◽  
T.J. Allanazarova
Keyword(s):  
Vries Equation ◽  
De Vries ◽  
Loaded Term

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

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