Reduced Three-Wave Model To Study The Hard Transition To Chaotic Dynamics In Alfven Wave-Fronts

Abstract

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of
circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore
the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave
being linearly unstable and the other waves damped. In a reduced three-wave model (equal
damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative
phase), no matter how small the growth rate of the unstable wave there exists a parametric
domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This
hard transition in phase-space behavior occurs for left-hand (LH) polarized waves,
paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are
modulationally unstable.