Higher-order solution of an electron-acoustic solitary waves with non-thermal electrons

Higher-order nonlinearity and dispersion to nonlinear electron acoustic waves are studied using the reductive perturbation method in an unmagnetized collisionless plasma consisting of a cold electron fluid and non-thermal hot electrons and stationary ions. Beside the KdV equation obtained from the lowest order of perturbation, a linear inhomogeneous (KdV-type) equation accounting for the higher-order nonlinearity and dispersion is derived. A stationary solution for equations resulting from higher order perturbation theory has been found using the renormalization method. The effect of higher-order correction and the energetic population parameter δ on the amplitude and width of the soliton are also discussed.