Investigating the effect of integration constants and various plasma parameters on the dynamics of the soliton in different physical plasmas

Abstract

The nonlinear dynamics and propagation of ion acoustic waves in a relativistic and ideal plasmas, which have the pressure variation of electrons and ions and degenerate electrons, are investigated using the analytic solution of KdV type equations performed applying (G′/G)-expansion and (G′/G,1/G)-expansion methods. The effects of various parameters, such as phase velocity of the ion acoustic wave, the ratio of ion temperature to electron temperature, normalized speed of light, electron and ion streaming velocities, arbitrary and integration constants, on the soliton dynamics are studied. We have found that dim and hump solitons and their amplitudes, widths and dynamics strongly depend on these plasma parameters and integration constants. The source term μ plays also a vital role in the formation of the solitons. Moreover, it is also found that the observed solitary wave solution can be excited from hump soliton to dip soliton. This dramatic change of the solitons can occur due to the various values of the integration constants and ion streaming velocities. Finally, it is important to note that the analytic solutions of the nonlinear equation, reported in this study, could be used to explain the structures of solitons in the astrophysical space and in laboratory plasmas.

New exact solutions of a nonlinear integrable equation

“…Nonlinear partial differential equations (NPDEs) are consequences of the mathematical models of problems arising in various fields of science. Among these equations, KdV and KdV typed equations can be applied to many important applications in physics and other fields of science . In order to provide a better understanding of the integrable systems, Wazwaz, in his article, used an integrable nonlinear KdV equation by combining the KdV recursion operator and the negative‐order recursion operator, where u = u ( x , t ).…”

Exact solutions for two different non-linear partial differential equations

“…As a pioneer work Li et al [15] has applied the two-variable (G ′ /G, 1/G)-expansion method and found the exact solutions of Zakharov equations. Some applications of the (G ′ /G, 1/G)-expansion method can be seen in [16,17,18,19,20]. (1/G ′ )-expansion method introduced by Yokus [21] firstly.…”

Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas

“…The original (G /G)-expansion method is generalized to find (G /G, 1/G)-expansion method [13]. Some applications of (G /G)-expansion method can be seen in [14][15][16][17][18]. As a pioneer work [19] has applied the two-variable (G /G, 1/G)-expansion method and found the exact solutions of Zakharov equations.…”