Perturbation Method for a Nonlinear Wave Modulation. II

Taniuti, Tosiya; Yajima, Nobuo

doi:10.1063/1.1664797

Cited by 254 publications

(86 citation statements)

References 2 publications

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“…We have shown that the slow variation of the wave's amplitude in space and time may be modeled via the longestablished multiple scale ("reductive perturbation") method Asano et al, 1969). One thus obtains explicit conditions for the occurrence of "modulational instability", which is related to wave collapse, or may possibly result in the formation of "localized envelope structures".…”

Section: Discussionmentioning

confidence: 99%

“…What follows is essentially an implementation of the long known "reductive perturbation" technique Asano et al, 1969;Shimizu and Ichikawa, 1972;Kako, 1974;Kakutani, 1974), which was first applied in the study of electron plasma Asano et al, 1969) and electron-cyclotron (Hasegawa 1970(Hasegawa , 1972 waves, more than three decades ago.…”

Section: Weakly Nonlinear Oscillation Regimementioning

confidence: 99%

See 1 more Smart Citation

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Kourakis

Shukła

2005

Nonlin. Processes Geophys.

142

161

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Abstract. Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave.A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrödinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright-(pulses) or dark-(holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.

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Section: Discussionmentioning

confidence: 99%

Section: Weakly Nonlinear Oscillation Regimementioning

confidence: 99%

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Kourakis

Shukła

2005

Nonlin. Processes Geophys.

142

161

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“…We employ a multiple-scale perturbation technique [62,63] to derive the evolution equation of a slowly varying weakly nonlinear wave amplitude of IAW packets in a q nonextensive plasma. Here, we consider A as the state vector {A}(= n i , u i , φ), describing the system's state at a given position x and time t. Small deviations will be considered from the equilibrium state…”

Section: Derivation Of Nls Equation: Pertubative Approachmentioning

confidence: 99%

Modulation of ion-acoustic waves in a nonextensive plasma with two-temperature electrons

2015

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We study the amplitude modulation of ion-acoustic wave (IAW) packets in an unmagnetized electron-ion plasma with two-temperature (cool and hot) electrons in the context of the Tsallis' nonextensive statistics. Using the multiple-scale technique, a nonlinear Schrödinger (NLS) equation is derived which governs the dynamics of modulated wave packets. It is shown that in nonextensive plasmas, the IAW envelope is always stable for long-wavelength modes (k → 0) and unstable for short-wavelengths with k > ∼ 1. However, the envelope can be unstable at an intermediate scale of perturbations with 0 < k < 1. Thus, the modulated IAW packets can propagate in the form of bright envelope solitons or rogons (at small-and medium scale perturbations) as well as dark envelope solitons (at large scale). The stable and unstable regions are obtained for different values of temperature and density ratios as well as the nonextensive parameters qc and q h for cool and hot electrons. It is found that the more (less) the population of superthermal cool (hot) electrons, the smaller is the growth rate of instability with cutoffs at smaller wave numbers of modulation.

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“…The standard method for studying this mechanism is a multiple space and time scale technique [6,7], which leads to a nonlinear Schrödinger-type equation (NLSE) describing the evolution of the wave envelope. It has been shown that, under certain conditions, waves may develop a Benjamin-Feir-type (modulational) instability (MI), i.e.…”

Section: Introductionmentioning

confidence: 99%

Oblique Amplitude Modulation of Dust-Acoustic Plasma Waves

Kourakis¹,

Shukła

2004

Phys. Scr.

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Theoretical and numerical studies are presented of the nonlinear amplitude modulation of dustacoustic (DA) waves propagating in an unmagnetized three component, weakly-coupled, fully ionized plasma consisting of electrons, positive ions and charged dust particles, considering perturbations oblique to the carrier wave propagation direction. The stability analysis, based on a nonlinear Schrödinger-type equation (NLSE), shows that the wave may become unstable; the stability criteria depend on the angle θ between the modulation and propagation directions. Explicit expressions for the instability rate and threshold have been obtained in terms of the dispersion laws of the system. The possibility and conditions for the existence of different types of localized excitations have also been discussed.

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Perturbation Method for a Nonlinear Wave Modulation. II

Cited by 254 publications

References 2 publications

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Modulation of ion-acoustic waves in a nonextensive plasma with two-temperature electrons

Oblique Amplitude Modulation of Dust-Acoustic Plasma Waves

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