Abstract
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.
Highlights
Ion-acoustic wave consisting of nonlinear phenomena and appearing in the different plasma systems [1] and fluid mechanics [2] is one of the fundamental problems
We have investigated the types of the solitary waves and the effect of plasma parameters and integration constants on the solitary waves in the four-component dusty space plasma using three different methods (G′/G)-expansion method, (G′/G, 1/G)-expansion method, and direct integration
We have numerically examined the types of solitons and their dynamical responds to the different plasma parameters and integration constants
Summary
Ion-acoustic wave consisting of nonlinear phenomena and appearing in the different plasma systems [1] and fluid mechanics [2] is one of the fundamental problems. It would be interesting to obtain the different forms of the traveling wave solutions of the Schamel-KdV equation These exact solutions may be used to explain the properties of the ion-acoustic waves arised in laboratory and astrophysical plasmas. The authors of [27] used the reductive perturbation method to derive the Schamel-KdV equation and investigated the effects of plasma parameters, ratio of ion to electron temperatures, mass and charge ratio, and the ratio of dust to ion temperatures, on solitary wave. They had found the compressive and rarefactive solitons.
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