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 negatively charged dust as well as distributed nonisothermal electrons are investigated by using the exact traveling wave solutions of the Schamel-KdV equation. The analytic solutions 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 phase speed $V_p$, plasma parameters $\alpha$, $\sigma$, and $\sigma_d$, and the source term $\mu$ are studied. We have observed different types of waves from the different analytic solutions obtained from the different methods. Consequently, we have found the discontinuity, shock or solitary waves. It is also concluded that these parameters play an important role in the presence of solitary waves inside the plasma. Depending on plasma parameters, the discontinuity wave turns into solitary wave solution for the certain values of the phase speed and plasma parameters. Additionally, exact solutions of the Schamel-KdV equation may also be used to understand the wave types and properties in the different plasma systems.

Anahtar Kelimeler:

Schamel-KdV equation, Dusty space plasma, Shock wave, Soliton

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