Journal ArticleDOI
A numerical study of nonlinear Alfvén waves and solitons
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In this paper, a split-step Fourier method was used to solve the derivative nonlinear Schrodinger equation (DNSE) for finite-amplitude Alfven waves.Abstract:
Finite‐amplitude Alfven waves can be modeled by a nonlinear wave equation termed the derivative nonlinear Schrodinger equation. A computer program has been developed that solves the derivative nonlinear Schrodinger equation via the ‘‘split‐step’’ Fourier method. This program has been used to investigate a number of topics in the area of nonlinear Alfven waves. When analytic envelope solitons are used as initial conditions, the wave packets propagate without distortion and with the expected speed–amplitude relation. When an arbitrary, amplitude‐modulated wave is used as an initial condition, the results depend strongly on the β of the plasma and the polarization of the wave. For a left circularly polarized wave in a β 1, a collapse instability has been observed in which the wave amplitude increases and modulation scale decreases. For other combinations of polarization and value of β, the wave packet tends to broaden, eliminating the initial modulation.read more
Citations
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Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations
TL;DR: In this paper, the existence and multiplicity of coherent structures in the complex Ginzburg-Landau equation was studied. But the authors focused on the competition between fronts and pulses and did not consider the non-uniformly translating front structures.
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Decay instability of finite-amplitude circularly polarized Alfven waves - A numerical simulation of stimulated Brillouin scattering
TL;DR: In this paper, an energy transfer from the parent wave to two daughter Alfven-like waves and a sound-like wave is observed (a stimulated Brillouin scattering process), and the observed growth rates and propagation characteristics of these daughter waves agree with the analytical results.
Journal ArticleDOI
High-resolution sounding rocket observations of large-amplitude Alfven waves
TL;DR: Shear Alfven waves with amplitudes greater than 100 mV/m were observed on two recent sounding rocket flights as mentioned in this paper, showing a downward propagation direction and implying insignificant reflection from the ionosphere at frequencies greater than 1 Hz.
Journal ArticleDOI
Nonlinear, dispersive, elliptically polarized Alfvén waves
TL;DR: In this paper, the derivative nonlinear Schrodinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables and an expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained.
Journal ArticleDOI
Modulation instability of circularly polarized Alfvén waves
M. Longtin,B. U. Ö. Sonnerup +1 more
TL;DR: In this article, the stability of a finite amplitude circularly polarized Alfven wave of wave number k0 was studied by using the two-fluid isentropic equations, and a surface was found that separated stable and unstable regions in parameter space.
References
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Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Journal ArticleDOI
Linear and Nonlinear Waves
G. B. Whitham,T. C. T. Ting +1 more
TL;DR: In this paper, a reference record was created on 2005-11-18, modified on 2016-08-08 and used for the purpose of ondes ; chocs ; onde de : choc reference record.
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On the modulational instability of hydromagnetic waves parallel to the magnetic field
TL;DR: In this paper, the stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. And the authors show that finite amplitude always promotes stability, while amplitude dependent stability conditions for long waves, previously obtained by the author, are confirmed.
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Nonlinear evolution of parallel‐propagating hydromagnetic waves
TL;DR: In this paper, the nonlinear evolution of plane hydromagnetic fluctuations propagating along the unperturbed magnetic field direction is considered and explicit expressions are derived for the asymptotic state and for the characteristic lines which describe the evolution toward that state.
Journal ArticleDOI
Properties of Alfvén solitons in a finite-beta plasma
TL;DR: In this article, the properties of Alfven solitons were examined in the case when the plasma possesses a finite pressure, and an envelope soliton was found which possesses a width-amplitude relationship.