Large-amplitude solitary waves in a relativistic nonisothermal plasma with warm ions

2000 ◽  
Vol 78 (4) ◽  
pp. 267-275
Author(s):  
R Roychoudhury ◽  
P Chatterjee
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Relativistic Effect ◽  
Soliton Solutions ◽  
Critical Value ◽  
Ion Temperature ◽  
52.35 Tc ◽  
Nonisothermal Plasma ◽  
52.35 Fp

Large amplitude solitary waves in a relativistic plasma with non-isothermal electrons and finite ion temperature are studied using Sagdeev's pseudopotential technique. It is found that there exists a critical value of beta, the ratio of the temperatures of the free and trapped electrons respectively, beyond which soliton solutions cease to exist. This critical value depends on other parameters. Also the relativistic effect and finite ion temperature restrict the region of existence of solitary waves. A small amplitude expansion of the pseudopotential is derived to find different kinds of solitary waves.PACS Nos.: 52.35 Fp, 52.35 Sb, 52.35 Tc

Speed and Shape of Solitary Waves in Two-electron Plasmas with Relativistic Warm Ions

2004 ◽  
Vol 59 (6) ◽  
pp. 353-358 ◽  
Author(s):  
Prasanta Chatterjee
Keyword(s):  
Solitary Waves ◽  
Electron Concentration ◽  
Large Amplitude ◽  
Critical Value ◽  
Relativistic Plasma ◽  
Hot Electron ◽  
Cold Electron ◽  
Ion Temperature ◽  
Electron Plasmas ◽  
Two Temperature

Large amplitude solitary waves are investigated in a relativistic plasma with finite ion-temperature and two temperature isothermal electrons. Sagdeev’s pseudopotential is determined in terms of the ion speed u. It is found that there exists a critical value of u0, the value of u at which (u’)2 = 0, beyond which the solitary waves cease to exists. The critical value also depends on parameters like the soliton velocity v, the fraction of the cold electron concentration μ, or the ratio of the cold and hot electron temperatures β .

Large Amplitude Solitary Waves in a Four-Component Dusty Plasma with Nonthermal Ions

2008 ◽  
Vol 63 (7-8) ◽  
pp. 393-399 ◽  
Author(s):  
Prasanta Chatterjee ◽  
Kaushik Roy
Keyword(s):  
Dusty Plasma ◽  
Solitary Waves ◽  
Soliton Solution ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Sagdeev Potential ◽  
Ion Distribution ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic ◽  
Pseudo Potential

Dust acoustic solitary waves are studied in a four-component dusty plasma. Positively and negatively charged mobile dust and Boltzmann-distributed electrons are considered. The ion distribution is taken as nonthermal. The existence of a soliton solution is determined by the pseudo-potential approach. It is shown that in small amplitude approximation our result obtained from the Sagdeev potential technique reproduce the result obtained by Sayed and Mamun [Phys. Plasmas 14, 014501 (2007)] provided one cosiders the nonthermal distribution for ions.

Arbitrary-amplitude electron acoustic solitary waves in a plasma

1995 ◽  
Vol 53 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Prasanta Chatterjee ◽  
Rajkumar Roychoudhury
Keyword(s):  
Solitary Waves ◽  
Numerical Technique ◽  
Soliton Solutions ◽  
Analytical Form ◽  
Complete Agreement ◽  
Ion Temperature ◽  
Sagdeev Potential ◽  
Arbitrary Amplitude ◽  
Pseudopotential Approach ◽  
Electron Acoustic

Recently Mace et at. studied electron-acoustic solitary waves in a plasma using a pseudopotential approach. To find the finite ion-temperature Sagdeev potential, they used a numerical technique developed by Baboolal, Bharuthram & Hellberg. In this paper we show that the exact pseudopotential can be obtained in this case in an analytical form. The numerical results obtained by Mace et at. are compared with our result, and complete agreement is found. We also discuss the conditions for the existence of solitary-wave solutions, and obtain the soliton solutions in some cases when these conditions are satisfied.

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.

Solitary waves on a vorticity layer

1994 ◽  
Vol 264 ◽  
pp. 303-319
Author(s):  
F. J. Higuera ◽  
J. Jiménez
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Symmetry Axis ◽  
Vries Equation ◽  
Continuous Family ◽  
Planar Case ◽  
Logarithmic Corrections ◽  
Spherical Vortex ◽  
The Waves

Contour dynamics methods are used to determine the shapes and speeds of planar, steadily propagating, solitary waves on a two-dimensional layer of uniform vorticity adjacent to a free-slip plane wall in an, otherwise irrotational, unbounded incompressible fluid, as well as of axisymmetric solitary waves propagating on a tube of azimuthal vorticity proportional to the distance to the symmetry axis. A continuous family of solutions of the Euler equations is found in each case. In the planar case they range from small-amplitude solitons of the Benjamin–Ono equation to large-amplitude waves that tend to one member of the touching pair of counter-rotating vortices of Pierrehumbert (1980), but this convergence is slow in two small regions near the tips of the waves, for which an asymptotic analysis is presented. In the axisymmetric case, the small-amplitude waves obey a Korteweg–de Vries equation with small logarithmic corrections, and the large-amplitude waves tend to Hill's spherical vortex.

Large-amplitude ion-acoustic waves in a plasma with a relativistic electron beam

1996 ◽  
Vol 56 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Yasunori Nejoh
Keyword(s):  
Electron Beam ◽  
Mach Number ◽  
Relativistic Electron ◽  
Acoustic Waves ◽  
Large Amplitude ◽  
Relativistic Electron Beam ◽  
Relativistic Effect ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Ion Acoustic

Nonlinear wave structures of large-amplitude ion-acoustic waves in a plasma with a relativistic electron beam are studied using the pseudopotential method. The region of existence of large-amplitude ion-acoustic waves is examined, and it is shown that the condition for their existence depends sensitively on parameters such as the relativistic effect of the electron beam, the ion temperature, the electrostatic potential and the electron beam density. It turns out that the region of existence spreads as the relativistic effect (Mach number) increases and the ion temperature decreases. New properties of large-amplitude ion-acoustic waves in a plasma with a relativistic electron beam are predicted.

Large-amplitude wavetrains and solitary waves in vortices

1990 ◽  
Vol 216 ◽  
pp. 459-504 ◽  
Author(s):  
S. Leibovich ◽  
A. Kribus
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Vortex Breakdown ◽  
Continuation Method ◽  
Soliton Solutions ◽  
Numerical Continuation ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Velocity Changes ◽  
Produce Flow

Large-amplitude axisymmetric waves on columnar vortices, thought to be related to flow structures observed in vortex breakdown, are found as static bifurcations of the Bragg–Hawthorne equation. Solutions of this equation satisfy the steady, axisymmetric, Euler equations. Non-trivial solution branches bifurcate as the swirl ratio (the ratio of azimuthal to axial velocity) changes, and are followed into strongly nonlinear regimes using a numerical continuation method. Four types of solutions are found: multiple columnar solutions, corresponding to Benjamin's ‘conjugate flows’, with subcritical–supercritical pairing of wave characteristics; solitary waves, extending previously known weakly nonlinear solutions to amplitudes large enough to produce flow reversals similar to the breakdown transition; periodic wavetrains; and solitary waves superimposed on the conjugate flow that emerge from the periodic wavetrain as the wavelength or amplitude becomes sufficiently large. Weakly nonlinear soliton solutions are found to be accurate even when the perturbations they cause are fairly strong.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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