Table of Contents
Journal of Astrophysics
Volume 2014 (2014), Article ID 812052, 15 pages
http://dx.doi.org/10.1155/2014/812052
Research Article

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

1Department of Aeronautics, Faculty of Exact, Physical and Natural Sciences, National University of Córdoba, Vélez Sarsfield 1611, X5016GCA Córdoba, Argentina
2National Council of Scientific and Technical Research (CONICET), Avenue Rivadavia 1917, C1033AAJ Buenos Aires, Argentina
3Institute of Theoretical and Experimental Astronomy (IATE-CONICET), Laprida 854, X5000BGR Córdoba, Argentina

Received 16 December 2013; Revised 6 March 2014; Accepted 10 March 2014; Published 14 April 2014

Academic Editor: Milan S. Dimitrijevic

Copyright © 2014 Gustavo Krause et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 Alfvén mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrödinger (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 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-wave truncation model fails due to the emergence of new nonnegligible modes.