Abstract
The DNLS equation describes weakly dispersive MHD waves propagating parallel as well as at a small angle to the magnetic field. For oblique propagation, the magnetosonic mode is described by the KdV equation, whereas certain aspects of the oblique Alfvén wave are described by the MKdV equation. The two latter equations possess one-parameter families of solitons. One-parameter families of oblique soliton solutions to the DNLS equation exist, which match to those of the KdV and MKdV in appropriate asymptotic limits. For parallel propagation, the DNLS equation possesses a well-known two-parameter family of soliton solutions. Such a family also exists in the oblique case (Kawata and Inoue, J. Phys. Soc. Japan 44, 1968 (1978)), but has so far been paid little attention. In the parallel case, soliton formation is known to result from modulational instability of circularly polarized wave trains. In the oblique case, a rich family of periodic wave train solutions exists which matches to the cnoidal solutions to MKdV and KdV in the appropriate limits. The modulational stability of these wave trains is studied by Whitman's method. A conjecture analogous to a result of Driscoll and O'Neil (Phys. Fluids 17, 1196 (1976)) is supported numerically.
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