Nonlinear, dispersive, elliptically polarized Alfvén waves

C. F. Kennel, B. Buti, Tohru Hada, R. Pellat

Research output: Contribution to journalArticle

Abstract

The derivative nonlinear Schrödinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. 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. The solitary wave solutions for elliptically polarized quasiparallel Alfvén waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg–de Vries and the modified Korteweg–de Vries solitons obtained previously for oblique propagation, but are more general. It is shown there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are charcterized.
Original languageEnglish
Article number10.1063/1.866642
Pages (from-to)1949-1961
Number of pages13
JournalPhysics of Fluids B
Volume31
Publication statusPublished - Jun 1988

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Solitons
solitary waves
Derivatives
Boundary conditions
boundary conditions
Magnetohydrodynamics
Nonlinear equations
infinity
magnetohydrodynamics
nonlinear equations
envelopes
propagation

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Kennel, C. F., Buti, B., Hada, T., & Pellat, R. (1988). Nonlinear, dispersive, elliptically polarized Alfvén waves. Physics of Fluids B, 31, 1949-1961. [10.1063/1.866642].

Nonlinear, dispersive, elliptically polarized Alfvén waves. / Kennel, C. F.; Buti, B.; Hada, Tohru; Pellat, R.

In: Physics of Fluids B, Vol. 31, 10.1063/1.866642, 06.1988, p. 1949-1961.

Research output: Contribution to journalArticle

Kennel, CF, Buti, B, Hada, T & Pellat, R 1988, 'Nonlinear, dispersive, elliptically polarized Alfvén waves', Physics of Fluids B, vol. 31, 10.1063/1.866642, pp. 1949-1961.
Kennel CF, Buti B, Hada T, Pellat R. Nonlinear, dispersive, elliptically polarized Alfvén waves. Physics of Fluids B. 1988 Jun;31:1949-1961. 10.1063/1.866642.
Kennel, C. F. ; Buti, B. ; Hada, Tohru ; Pellat, R. / Nonlinear, dispersive, elliptically polarized Alfvén waves. In: Physics of Fluids B. 1988 ; Vol. 31. pp. 1949-1961.
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AB - The derivative nonlinear Schrödinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. 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. The solitary wave solutions for elliptically polarized quasiparallel Alfvén waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg–de Vries and the modified Korteweg–de Vries solitons obtained previously for oblique propagation, but are more general. It is shown there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are charcterized.

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