摘要：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 coupling of three
waves near resonance, one wave being linearly unstable and the other waves
damped. No matter how small the growth rate of the unstable wave, the
four-dimensional flow for the three wave amplitudes and a relative phase,
with both resistive damping and linear Landau damping, exhibits chaotic
relaxation oscillations that are absent for zero growth-rate. This hard
transition in phase-space behavior occurs for left-hand (LH) polarized
waves, paralleling the known fact that only LH time-harmonic solutions of the
DNLS equation are modulationally unstable. The parameter domain developing
chaos is much broader than the corresponding domain in a reduced 3-wave model
that assumes equal dampings of the daughter waves.
