Propagation of nonlinear waves in a plasma in a magnetic field

1968 ◽  
Vol 2 (2) ◽  
pp. 105-118 ◽  
Author(s):  
Jeffrey P. Freidberg
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Local Density ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Resonant Frequencies ◽  
Wave Solutions ◽  
Nonlinear Dispersion Relation ◽  
The Waves ◽  
The Magnetic Field

The propagation of nonlinear electromagnetic waves in a plasma is investigated by seeking travelling wave solutions to the macroscopic plasma equations. The model considered is that of a warm, anisotropic electron plasma in a magnetic field, in which the waves are allowed to propagate at any angle with respect to the magnetic field. A nonlinear dispersion relation is obtained which is valid for frequencies sufficiently close to the resonant frequencies. Travelling wave solutions are found for all amplitudes for which the local density remains positive. Also in sufficiently anisotropic plasmas the nature (i.e. propagating or cut-off) of one of the resonant waves can depend upon the amplitude.

Using Compressibility and Electric Field to Characterize Circularly-Polarized Waves Near the Proton Cyclotron Frequency Observed by Solar Orbiter

2021 ◽  
Author(s):  
Yuri Khotyaintsev ◽  
Daniel B Graham ◽  
Konrad Steinvall ◽  
Andris Vaivads ◽  
Milan Maksimovic ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Electric Field ◽  
Electromagnetic Waves ◽  
Cyclotron Frequency ◽  
Density Fluctuations ◽  
Background Magnetic Field ◽  
The Waves ◽  
The Magnetic Field ◽  
Proton Cyclotron

<p>We report Solar Orbiter observations of electromagnetic waves near the proton cyclotron frequency during the first perihelion. The waves have polarization close to circular and have wave vectors closely aligned with the background magnetic field. Such waves are potentially important for heating of the solar wind as their frequency and polarization allows effective energy exchange with solar wind protons. The Radio and Plasma Waves (RPW) instrument provides a high-cadence measurement of plasma density and electric field which we use together with the magnetic field measured by MAG to characterize these waves. In particular we compute the compressibility and the phase between the density fluctuations and the parallel component of the magnetic field, and show that these have a distinct behavior for the waves compared to the Alfvénic turbulence. We compare the observations to multi-fluid plasma dispersion and identify the waves modes corresponding to the observed waves. We discuss the importance of the waves for solar wind heating.</p>

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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