Journal ArticleDOI
On the modulational instability of hydromagnetic waves parallel to the magnetic field
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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.Abstract:
The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.read more
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The Solar Wind as a Turbulence Laboratory
Roberto Bruno,Vincenzo Carbone +1 more
TL;DR: In this paper, the authors focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state.
Journal ArticleDOI
An exact solution for a derivative nonlinear Schrödinger equation
David J. Kaup,Alan C. Newell +1 more
TL;DR: In this paper, a method of solution for the derivative nonlinear Schrodinger equation is presented, where the appropriate inverse scattering problem is solved and the one-soliton solution is obtained, as well as the infinity of conservation laws.
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Optical Solitons
TL;DR: The theory of optical solitons as well as their experimental investigation has progressed rapidly as discussed by the authors, and optical soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field.
Journal ArticleDOI
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
A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative
TL;DR: In this paper, it was shown that the one-dimensional Schrodinger equation with derivative in the nonlinear term is globally well-posed in Hs for data small in L2.
References
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A general approach to linear and non-linear dispersive waves using a Lagrangian
TL;DR: In this article, a general theory is given for non-uniform wave trains whose amplitude, wave-number, etc., vary slowly in space and time, the length and time scales of the variation in amplitude and wave number, being large compared to the wavelength and period.
Book ChapterDOI
Wavetrains in Inhomogeneous Moving Media
TL;DR: In this article, it was shown that for a wide class of conservative systems in fluid dymamics changes in amplitude along the rays may be computed from conservation of wave action, defined as the wave energy divided by the intrinsic frequency.
Book
The theory of partial differential equations
TL;DR: In this article, Fourier series and Fourier transforms have been used to describe fundamental theory, evolution equations, and semi-linear hyperbolic equations, as well as a number of others.
Journal ArticleDOI
Reductive Perturbation Method in Nonlinear Wave Propagation. I
Tosiya Taniuti,Chau-Chin Wei +1 more
TL;DR: In this paper, a class of nonlinear partial differential equations which admit a reduction to tractable nonlinear equations such as the Burgers and the Kortweg-deVries equation is presented.
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