Stability of acoustic nonlinear dispersive eigenmodes

In an earlier investigation, spectral evolution equations were derived for nonlinear dispersive propagation. For the special case of two harmonics, two eigenmodes were shown to exist, of which one is parametric in nature. In this paper we develop a general method of stability analysis and show that in the case of two eigenmodes their limit cycle behavior is in agreement with earlier results obtained by different, less general, methods. We will also discuss the relation of the nonlinear eignmodes to cnoidal waves and acoustic solitons.