Axially symmetric propagation of small‐amplitude ion‐acoustic waves

1990 ◽  
Vol 2 (8) ◽  
pp. 1775-1779 ◽  
Author(s):  
Russell L. Herman
2020 ◽  
Vol 75 (3) ◽  
pp. 183-191 ◽  
Author(s):  
Durga Prasad Chapagai ◽  
Jharna Tamang ◽  
Asit Saha

AbstractBifurcation analysis of small-amplitude nonlinear and supernonlinear periodic ion-acoustic waves (SNPIAWs) is reported in a three-constituent superthermal plasma composing of cold fluid ions and kappa-distributed electrons of two temperatures (cold and hot). Using the reductive perturbation technique, the plasma system is studied under the Korteweg-de Vries (KdV) and the modified KdV (mKdV) equations. Furthermore, the KdV and mKdV equations are transformed into planar dynamical systems applying travelling wave transfiguration. Possible qualitative phase profiles for the corresponding dynamical systems controlled by system parameters ($\kappa,{\alpha_{c}},{\alpha_{h}}$ and f) are shown. Small-amplitude SNPIAW solution for the mKdV equation is presented for the first time. Small-amplitude nonlinear periodic ion-acoustic wave (NPIAW) and ion-acoustic solitary wave solutions (IASWS) for both the KdV and mKdV equations are obtained. Effects of parameters κ and αh on IASW, NPIAW and SNPIAW solutions are investigated.


1975 ◽  
Vol 13 (1) ◽  
pp. 139-145 ◽  
Author(s):  
Hans Schamel

Physically acceptable solutions of the time-independent Vlasov–Poisson system are found by applying a method which is analogous to the soliton method in Korteweg–de Vries theory. Cnoidal wave solutions for small-amplitude Langmuir and ion acoustic waves are derived, in which the nonlinearity is determined by trapped electrons. The class of weakly distorted waves is shown to be modulational unstable.


2009 ◽  
Vol 27 (4) ◽  
pp. 1457-1467 ◽  
Author(s):  
R. G. Michell ◽  
K. A. Lynch ◽  
C. J. Heinselman ◽  
H. C. Stenbaek-Nielsen

Abstract. Observations of naturally enhanced ion acoustic lines (NEIALs) taken with the Poker Flat Incoherent Scatter Radar (PFISR) using a mode with very high time resolution are presented. The auroral event took place over Poker Flat, Alaska on 8 February 2007 at 09:35 UT (~22:00 MLT), and the radar data are complemented by common-volume high-resolution auroral imaging. The NEIALs occurred during only one of the standard 15-s integration periods. The raw data of this time show very intermittent NEIALs which occur only during a few very short time intervals (≤1 s) within the 15-s period. The time sampling of the raw data, ~19 ms on average, allows study of the time development of the NEIALs, though there are indications that even finer time resolution would be of interest. The analysis is based on the assumption that the NEIAL returns are the result of Bragg scattering from ion-acoustic waves that have been enhanced significantly above thermal levels. The spectra of the raw data indicate that although the up- and down-shifted shoulders can both become enhanced at the same time, (within 19 ms), they are most often enhanced individually. The overall power in the up-and down-shifted shoulders is approximately equal throughout the event, with the exception of one time, when very large up-shifted power was observed with no corresponding down-shifted power. This indicates that during the 480 μs pulse, the strongly enhanced ion-acoustic waves were only traveling downward and not upward. The exact time that the NEIALs occurred was when the radar beam was on the boundary of a fast-moving (~10 km/s), bright auroral structure, as seen in the high resolution auroral imaging of the magnetic zenith. When viewed with high time resolution, the occurrence of NEIALs is associated with rapid changes in auroral luminosity within the radar field of view due to fast-moving auroral fine structures.


Author(s):  
Anne de Bouard

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.


1985 ◽  
Vol 44 (8) ◽  
pp. 537-543 ◽  
Author(s):  
E. Infeld ◽  
P. Frycz ◽  
T. Czerwiśka-Lenkowska

2016 ◽  
Vol 23 (8) ◽  
pp. 082901 ◽  
Author(s):  
T. Sreeraj ◽  
S. V. Singh ◽  
G. S. Lakhina

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