Nonlinear waves and coherent structures in quasi-neutral plasmas excited by external electromagnetic radiation

Stephan I. Tzenov

doi:10.1063/1.5003322

Nonlinear waves and coherent structures in quasi-neutral plasmas excited by external electromagnetic radiation

Physics of Plasmas ◽

10.1063/1.5003322 ◽

2017 ◽

Vol 24 (12) ◽

pp. 123105 ◽

Cited By ~ 3

Author(s):

Stephan I. Tzenov

Keyword(s):

Electromagnetic Radiation ◽

Coherent Structures ◽

Nonlinear Waves

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Nonlinear Waves and Coherent Structures in Laser Induced Plasmas and Polarized Vacuum

Physics of Particles and Nuclei ◽

10.1134/s1063779620050081 ◽

2020 ◽

Vol 51 (5) ◽

pp. 942-964

Author(s):

Stephan I. Tzenov

Keyword(s):

Coherent Structures ◽

Nonlinear Waves

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Bifurcations and nonlinear dynamics of surface waves in Faraday resonance

Journal of Fluid Mechanics ◽

10.1017/s0022112095000383 ◽

1995 ◽

Vol 284 ◽

pp. 341-358 ◽

Cited By ~ 16

Author(s):

H. Friedel ◽

E. W. Laedke ◽

K. H. Spatschek

Keyword(s):

Nonlinear Dynamics ◽

Solitary Wave ◽

Resonant Frequency ◽

Coherent Structures ◽

Nonlinear Waves ◽

Vertical Oscillation ◽

Spatial Structures ◽

Spatial Chaos ◽

Long Channel ◽

Solitary Form

The nonlinear dynamics of nonlinear modulated cross-waves of resonant frequency ω1 and carrier frequency ω ≈ ω1 is investigated. In a long channel of width b, that contains fluid of depth d and which is subjected to a vertical oscillation of frequency 2ω, the wave can appear in solitary form. As has been shown previously, the solitary wave is only stable in a certain parameter regime; depending on damping and driving amplitudes the wave becomes unstable. The nonlinear development of the instabilities of solitary waves is the central problem of this paper. It is shown how instabilities are saturated following generic routes to chaos in time with spatially coherent structures. Finally, the case of time-modulated driving amplitudes is also considered. In most cases it appears that nonlinear waves of simple spatial structures take part in the nonlinear dynamics, but a few cases of spatial chaos are also reported.

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Short-wavelength ion Bernstein nonlinear waves and solitons

Journal of Plasma Physics ◽

10.1017/s0022377800027185 ◽

1994 ◽

Vol 52 (3) ◽

pp. 353-364

Author(s):

T. A. Davydova ◽

A. I. Fishchuk ◽

V. M. Lashkin

Keyword(s):

Nonlinear Equation ◽

Analytical Solutions ◽

Coherent Structures ◽

Nonlinear Waves ◽

Short Wavelength ◽

Space Plasmas ◽

Periodic Waves ◽

Envelope Solitons

Short-wavelength coherent structures of ion Bernstein modes are studied on the basis of a nonlinear equation taking into account the effect of high-frequencey diamagnetism. Analytical solutions in the form of nonlinear periodic waves and envelope solitons are found, and their properties are discussed. The appearance of such structures may explain some phenomena observed in laboratory and space plasmas.

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Stability of nonlinear waves and patterns and related topics

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2018.0001 ◽

2018 ◽

Vol 376 (2117) ◽

pp. 20180001

Author(s):

Anna Ghazaryan ◽

Stephane Lafortune ◽

Vahagn Manukian

Keyword(s):

Coherent Structures ◽

Nonlinear Waves ◽

Dynamic Properties ◽

Travelling Waves ◽

Complex Structure ◽

Nonlinear Partial Differential Equations ◽

Theme Issue ◽

Hybrid Techniques ◽

Wave Trains ◽

The Waves

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

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