Chaos and Intermittency in the DNLS Equation Describing the Parallel Alven Wave e Propagation

KRAUSE, GUSTAVO; ELASKAR, SERGIO; COSTA, ANDREA

Journal of Astrophysics

Hindawi Publishing Corporation (ISSN: 2314-6192)

Lugar: New York ; Año: 2014 vol. 2014

2356-718X

When parallel to the ambient magnetic field propagation is considered in the Magnetohydrodynamics equations with Hall effect (Hall-MHD model), the Alfven mode deacouples from the magnetosonic modes and then, the waves are circularly polarized being described by the derivative non linear Schrodinger (DNLS) equation. In this paper, we numerically solve the DNLS equation using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, we test the validity of the method by verifying the analytical condition of mod-ulational stability for the non-diffusive case. Later, we incorporate diffusive and excitatory effects comparing the numerical results with those obtained by a three-mode truncation model. We show that different types of attractors can exist depending on the diffusion level: for relatively large damping there are fixed points for which the truncation model is a good approximation; for low damping chaotic solutions appear and the three-mode truncation model fails due to the emergenceof new non-negligible modes.