Explicit, periodic and dispersive soliton solutions to the Schamel-KdV equation with constant coefficients

Abstract

In plasma physics, the Schamel–Korteweg-de Vries (S-KdV) model determines the electrostatic potential for a given electron distribution in velocity space and is used to explore ion acoustic solitons during the trapping of electrons. The key model reduces to the generalised KdV equation for α=0, and the Schamel equation when β=0. In this article, some new traveling wave solutions to the Schamel-KdV equation are constructed with the help of the classical Khater and the modified Khater methods. The observed results are very encouraging, which provide more powerful mathematical tool for analyzing exact traveling wave solution to the nonlinear equations arising in the recent era of applied sciences and engineering.