Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation

GUSTAVO J. KRAUSE; SERGIO ELASKAR; ANDREA COSTA

Journal of Astrophysics

Hindawi Publishing Corporation

Año: 2014 vol. 2014 p. 1 - 15

2356-718X

When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model) the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfv ́n mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrodinger (DNLS) equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on thediffusion 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-wave truncation model fails due to the  emergence of new nonnegligible modes.