On the modulational instability of hydromagnetic waves parallel to the magnetic field

TLDR

The stability of circularly polarized finite‑amplitude waves propagating parallel to the magnetic field is investigated. A set of equations for slowly varying waves of arbitrary amplitude is derived, and their stability is analyzed using these equations. Finite amplitude always promotes stability, confirming earlier results and validating an amplitude‑dependent stability condition for long waves.

Abstract

The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.