Analysis of the dispersion function for anisotropic longitudinal plasma waves

An analysis of the zeros of the dispersion function for longitudinal plasma waves is made. In particular, the plasma equilibriumdistribution function is assumed to have two relative maxima and is not necessarily an even function. The results of this analysis are used to obtain the Wiener–Hopf factorization of the dispersion function. A brief analysis of the coupled nonlinear integral equations for the Wiener–Hopf factors is also presented.