Oblique Reflection of Solitons in an Inhomogeneous Plasma: Effect of Trapped Electrons

Abstract

This paper aims at studying the oblique reflection of solitons in an inhomogeneous plasma having finite-temperature ions and trapped electrons (two-temperature nonisothermal electrons). In order to study the soliton reflection, a coupled equation is derived based on modified Korteweg-deVries equations for the incident and reflected solitons, and then, it is solved along with the use of incident soliton solution. The expressions for the reflected soliton amplitude, width, and reflection coefficient are obtained and examined for different parameter regimes. The reflection coefficient, which is the ratio of reflected and incident soliton amplitudes, is found to be independent of the ion and electron temperatures. It infers that both the amplitudes change in the same proportion with the ion and electron temperatures. It is observed that the soliton reflects with higher amplitude when the obliqueness is smaller. It is also seen that the reflected soliton undergoes a downshift in its original line of propagation. This downshift is further investigated in detail. The effect of the trapped electrons on the soliton reflection characteristics and on the downshift is also analyzed.

Evolution of solitons and their reflection and transmission in a plasma having negatively charged dust grains

“…However, for the sake of simplicity we assume that the direction of propagation of the reflected soliton is opposite to the directions of propagation of the incident and transmitted solitons, i.e., the transmission of the soliton is considered in the same direction as that of the incident soliton. Hence, the stretched coordinates for the incident wave are taken as [5,11,27,33] …”

“…(12). To analyze these structures, we use a sine-cosine method [4,5,34] because the solution of mKdV equations cannot be determined by ordinary methods due to presence of variable coefficients. For this, we put (12) and get…”

“…Washimi and Taniuti [1] were the first to derive the well-known Korteweg-deVries (KdV) equation with the help of reductive perturbation technique (RPT) to describe the soliton behavior in the homogeneous plasma. However, plasma contributes an extra term in the usual KdV equation [2][3][4][5], when the density inhomogeneity is taken into account, and then modified KdV (mKdV) equation is realized. Accordingly, the soliton behavior is modified in the inhomogeneous plasmas.…”