### Abstract

Original language | English |
---|---|

Article number | 10.1063/1.866642 |

Pages (from-to) | 1949-1961 |

Number of pages | 13 |

Journal | Physics of Fluids B |

Volume | 31 |

Publication status | Published - Jun 1988 |

### Fingerprint

### Cite this

*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.

Research output: Contribution to journal › Article

*Physics of Fluids B*, vol. 31, 10.1063/1.866642, pp. 1949-1961.

}

TY - JOUR

T1 - Nonlinear, dispersive, elliptically polarized Alfvén waves

AU - Kennel, C. F.

AU - Buti, B.

AU - Hada, Tohru

AU - Pellat, R.

PY - 1988/6

Y1 - 1988/6

N2 - 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.

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.

M3 - Article

VL - 31

SP - 1949

EP - 1961

JO - Physics of Fluids B

JF - Physics of Fluids B

SN - 0899-8221

M1 - 10.1063/1.866642

ER -