Effect of higher-order nonlinearity to nonlinear electron-acoustic solitary waves in an unmagnetized collisionless plasma

The contribution of the higher-order nonlinearity to nonlinear electron acoustic waves in an unmagnetized collisionless plasma consisting of a cold electron fluid and hot electrons obeying a trapped vortex-like distribution, and stationary ions is studied by use of the reductive perturbation method. A modified Korteweg-de Vries (mKdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (mKdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effect of higher-order nonlinearity on the amplitude of the soliton are also discussed.