Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

The wave properties in a dusty space plasma consisting of positively and negativelycharged dust as well as distributed nonisothermal electrons are investigated byusing the exact traveling wave solutions of the schamel-kdv equation. the analyticsolutions are obtained by the different types (g′/g)-expansion methods and direct integration.the nonlinear dynamics of ion-acoustic waves for the various values of phasespeed vp, plasma parameters a, s , and sd, and the source term m are studied. we haveobserved different types of waves from the different analytic solutions obtained fromthe different methods. consequently, we have found the discontinuity, shock or solitarywaves. it is also concluded that these parameters play an important role in the presenceof solitary waves inside the plasma. depending on plasma parameters, the discontinuitywave turns into solitary wave solution for the certain values of the phase speed andplasma parameters. additionally, exact solutions of the schamel-kdv equation may alsobe used to understand the wave types and properties in the different plasma systems.