Soliton Theory of Quasi-Parallel MHD Waves

E. Mjølhus, Tohru Hada

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Abstract

There has been some attention to soliton theory for MHD waves in the space plasma community; in particular, the DNLS equation, which describes the behavior of quasi parallel weakly nonlinear and weakly dispersive MHD waves, has been emphasized. Some of the virtues of this model are that (i) there is an abundance of known exact solutions, and (ii) it contains the KdV, MKdV and NLS equations as limiting cases. In this text, the properties of the DNLS equation is reviewed: its physical significance, the exact solutions, its IST, and the soliton formation processes. Finally, the process of dispersive steepening as described by the DNLS equation, is discussed; a combined process of modulational instability and nonlinear Landau damping is described, and the oblique two-parameter solitons are for the first time exhibited in detail.
Original languageEnglish
Title of host publicationNonlinear Waves and Chaos in Space Plasmas
EditorsT. Hada, H. Matsumoto
Place of PublicationTokyo
PublisherTerra Scientific Publishing Company
Pages121-169
Number of pages49
ISBN (Print)4-88704-121-7
Publication statusPublished - 1997

Fingerprint

solitary waves
space plasmas
Landau damping

Cite this

Mjølhus, E., & Hada, T. (1997). Soliton Theory of Quasi-Parallel MHD Waves. In T. Hada, & H. Matsumoto (Eds.), Nonlinear Waves and Chaos in Space Plasmas (pp. 121-169). Tokyo: Terra Scientific Publishing Company.

Soliton Theory of Quasi-Parallel MHD Waves. / Mjølhus, E. ; Hada, Tohru.

Nonlinear Waves and Chaos in Space Plasmas. ed. / T. Hada; H. Matsumoto. Tokyo : Terra Scientific Publishing Company, 1997. p. 121-169.

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Mjølhus, E & Hada, T 1997, Soliton Theory of Quasi-Parallel MHD Waves. in T Hada & H Matsumoto (eds), Nonlinear Waves and Chaos in Space Plasmas. Terra Scientific Publishing Company, Tokyo, pp. 121-169.
Mjølhus E, Hada T. Soliton Theory of Quasi-Parallel MHD Waves. In Hada T, Matsumoto H, editors, Nonlinear Waves and Chaos in Space Plasmas. Tokyo: Terra Scientific Publishing Company. 1997. p. 121-169
Mjølhus, E. ; Hada, Tohru. / Soliton Theory of Quasi-Parallel MHD Waves. Nonlinear Waves and Chaos in Space Plasmas. editor / T. Hada ; H. Matsumoto. Tokyo : Terra Scientific Publishing Company, 1997. pp. 121-169
@inbook{64bc8830376a410da231394d5fdd00c8,
title = "Soliton Theory of Quasi-Parallel MHD Waves",
abstract = "There has been some attention to soliton theory for MHD waves in the space plasma community; in particular, the DNLS equation, which describes the behavior of quasi parallel weakly nonlinear and weakly dispersive MHD waves, has been emphasized. Some of the virtues of this model are that (i) there is an abundance of known exact solutions, and (ii) it contains the KdV, MKdV and NLS equations as limiting cases. In this text, the properties of the DNLS equation is reviewed: its physical significance, the exact solutions, its IST, and the soliton formation processes. Finally, the process of dispersive steepening as described by the DNLS equation, is discussed; a combined process of modulational instability and nonlinear Landau damping is described, and the oblique two-parameter solitons are for the first time exhibited in detail.",
author = "E. Mj{\o}lhus and Tohru Hada",
year = "1997",
language = "English",
isbn = "4-88704-121-7",
pages = "121--169",
editor = "Hada, {T. } and Matsumoto, {H. }",
booktitle = "Nonlinear Waves and Chaos in Space Plasmas",
publisher = "Terra Scientific Publishing Company",
address = "Japan",

}

TY - CHAP

T1 - Soliton Theory of Quasi-Parallel MHD Waves

AU - Mjølhus, E.

AU - Hada, Tohru

PY - 1997

Y1 - 1997

N2 - There has been some attention to soliton theory for MHD waves in the space plasma community; in particular, the DNLS equation, which describes the behavior of quasi parallel weakly nonlinear and weakly dispersive MHD waves, has been emphasized. Some of the virtues of this model are that (i) there is an abundance of known exact solutions, and (ii) it contains the KdV, MKdV and NLS equations as limiting cases. In this text, the properties of the DNLS equation is reviewed: its physical significance, the exact solutions, its IST, and the soliton formation processes. Finally, the process of dispersive steepening as described by the DNLS equation, is discussed; a combined process of modulational instability and nonlinear Landau damping is described, and the oblique two-parameter solitons are for the first time exhibited in detail.

AB - There has been some attention to soliton theory for MHD waves in the space plasma community; in particular, the DNLS equation, which describes the behavior of quasi parallel weakly nonlinear and weakly dispersive MHD waves, has been emphasized. Some of the virtues of this model are that (i) there is an abundance of known exact solutions, and (ii) it contains the KdV, MKdV and NLS equations as limiting cases. In this text, the properties of the DNLS equation is reviewed: its physical significance, the exact solutions, its IST, and the soliton formation processes. Finally, the process of dispersive steepening as described by the DNLS equation, is discussed; a combined process of modulational instability and nonlinear Landau damping is described, and the oblique two-parameter solitons are for the first time exhibited in detail.

M3 - Chapter (peer-reviewed)

SN - 4-88704-121-7

SP - 121

EP - 169

BT - Nonlinear Waves and Chaos in Space Plasmas

A2 - Hada, T.

A2 - Matsumoto, H.

PB - Terra Scientific Publishing Company

CY - Tokyo

ER -