Parallel Propagation of Nonlinear Low‐Frequency Waves in High‐β Plasma

A pair of coupled, nonlinear, partial differential equations which describe the evolution of low‐frequency, large‐scale‐length perturbations propagating parallel, or nearly parallel, to the equilibrium magnetic field in high‐β plasma have been obtained. The equations account for irreversible resonant particle effects. In the regime of small but finite propagation angles, the pair of equations collapses into a single Korteweg‐de Vries equation (neglecting irreversible terms) which agrees with known results.