Effects of higher-order nonlinearity and finite geometry on the propagation of KdV solitons

Using reductive perturbation theory and a planar waveguide geometry, the effects of higher-order nonlinearity and finite boundaries on the propagation of electron plasma and ion-acoustic KdV solitons are investigated by taking into account finite electron and ion temperatures. For an electron plasma wave, the higher-order nonlinearity is found to increase the amplitude of the soliton and slightly decrease the width of the soliton compared with that predicted by the first-order theory. For an ion-acoustic wave the higher-order-nonlinearity and finite-boundary effects give rise to a W-shaped soliton.