Soliton Theory of Quasi-Parallel MHD Waves

E. Mjølhus, Tohru Hada

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


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
Number of pages49
ISBN (Print)4-88704-121-7
Publication statusPublished - 1997


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