Higher Order Corrections on the Plasma Wave Characteristics with Cairns–Gurevich Distribution

The propagation of electron-acoustic waves in a collisionless unmagnetized plasma composed of hot electrons obeying the Cairns–Gurevich (CG) distribution, inertial cold electrons and stationary ions are considered. The basic field equations of the above described plasma is re-examined through the use of the modified Poincare–Lighthill–Kuo (PLK) method. Introducing the strained coordinates and expanding the field quantities into the parameter \(\epsilon \), a set of differential equations is obtained. The lowest order term in the perturbation expansion is governed by the modified KdV equation, whereas the second order term is governed by the modified linearized KdV equation with nonhomogeneous term. Then, studying the localized travelling wave solution for the evolution equations, the strained coordinates for this order is determined so as to remove the possible secularities that might occur in the solution. It is observed that the ratio of the second order term to the first order term in the perturbation expansion is negative and not so small. This is equivalent to saying that the contribution of second order term decreases the wave amplitude. In other words, retaining only the first order term in the perturbation expansion overestimates the real value of the field quantities.