Head-on collisions of electrostatic solitons in nonthermal plasmas

Abstract

In contrast to overtaking interactions, head-on collisions between two electrostatic solitons can only be dealt with by an approximate method, which limits the range of validity but offers valuable insights. Treatments in the plasma physics literature all use assumptions in the stretching of space and time and in the expansion of the dependent variables that are seldom if ever discussed. All models force a separability to lowest order, corresponding to two linear waves with opposite but equally large velocities. A systematic exposition of the underlying hypotheses is illustrated by considering a plasma composed of cold ions and nonthermal electrons. This is general enough to yield critical compositions that lead to modified rather than standard Korteweg-de Vries equations, an aspect not discussed so far. The nonlinear evolution equations for both solitons and their phase shifts due to the collision are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is critical, rendering the nonlinearity in the evolution equations cubic, with concomitant repercussions on the phase shifts. In the latter case, the solitons can have either polarity, so that combinations of negative and positive solitons can occur, contrary to the generic case, where both solitons necessarily have the same polarity.

Theoretical study of head-on collision of dust acoustic solitary waves in a strongly coupled complex plasma

“…This fact has been well demonstrated and the technique successfully employed by several past authors studying head on collision of two solitary waves in various media. 20,23,25,26 For a detailed critique of the strengths and limitations of the method, the reader is referred to the paper by Verheest et al 25 Our main objective in this work is to assess the influence of strong coupling on these phase shifts and in the next section we present our results obtained using the above analytic relations (Eqs. (43) and (44)) for various plasma parameters.…”

“…[17][18][19][20][21][22][23][24][25][26] The observation that a discrete nonlinear system exhibits recurrent states instead of an ergodic behavior was explained by Zabusky and Kruskal, 17 who realized that the nonlinear chain is described by the KdV equation in the continuum limit. Thus, any deviation from KdV approximation in real systems will affect the thermalization time and break the recurrence of the initial state.…”

“…Many authors have investigated the head-on collision of two solitary waves in different plasma models using the extended Poincar e-Lighthill-Kuo (PLK) method. [20][21][22][23][24][25][26] In a dusty plasma, Xue 20 investigated the head-on collisions of dustacoustic solitary waves in an unmagnetized dusty plasma including the dust charge variation, and the analytical phase shifts following the head-on collision were derived. They showed the variation of phase shift with different plasma parameters.…”

Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

“…[52][53][54][55] According to this method, we obtain a set of equations governing the dynamics of the colliding solitary waves…”

Interaction phenomena and effect of higher order dispersion on electron acoustic solitary waves in weakly relativistic regimes

“…This ensures that the emission is related to the electron dynamics only. Over the last few years, a number of authors [23][24][25][26][27][28][29][30] have paid their attention to understand the interaction phenomena of non-linear waves in magnetized or unmagnetized plasmas taking different plasma conditions into account. A number of authors [14][15][16][17][18] have paid their attention to investigate the properties, such as solitary electron acoustic structures, creation of BEN by electron acoustic solitons (EASs), and so on of EAWs in unmagnetized plasmas.…”