Modulational Instability and Envelope-Solitons for Nonlinear Alfvén Waves Propagating along the Magnetic Field in Plasmas

Abstract

The modulational instability and envelope-solitons are analyzed for the Alfvén waves propagating along the static magnetic field in cold collisionless plasmas, using the modified nonlinear Schrödinger equation previously derived by the authors. The modulational instability occurs in the left-hand circularly polarized Alfvén wave (left Alfvén wave) for a small amplitude but does not for an amplitude larger than the critical value. On the other hand, the instability never occurs in the right-hand circularly polarized Alfvén wave (right Alfvén wave). When the modulational instability does not occur, the rarefactive and compressive envelope-solitons exist in the left Alfvén wave and the two types of the rarefactive envelope-solitons exist in the right Alfvén wave.