In this paper, we have studied linear and nonlinear propagation of electron acoustic waves (EAWs) comprising cold and hot populations in which the ions form the neutralizing background. The hot electrons have been assumed to follow the generalized (r,q) distribution which has the advantage that it mimics most of the distribution functions observed in space plasmas. Interestingly, it has been found that unlike Maxwellian and kappa distributions, the electron acoustic waves admit not only rarefactive structures but also allow the formation of compressive solitary structures for generalized (r,q) distribution. It has been found that the flatness parameter r, tail parameter q, and the nonlinear propagation velocity u affect the propagation characteristics of nonlinear EAWs. Using the plasmas parameters, typically found in Saturn's magnetosphere and the Earth's auroral region, where two populations of electrons and electron acoustic solitary waves (EASWs) have been observed, we have given an estimate of the scale lengths over which these nonlinear waves are expected to form and how the size of these structures would vary with the change in the shape of the distribution function and with the change of the plasma parameters.

In this paper, we have studied the linear and nonlinear propagation of ion acoustic waves in the presence of electrons that follow the generalized (r,q) distribution. It has been shown that for positive values of r, which correspond to a flat-topped electron velocity distribution, the nonlinear ion acoustic waves admit rarefactive solitary structures or density depletions. It has been shown that the generalized (r,q) distribution function provides another way to explicate the density depletions observed by Freja and Viking satellites previously explained by proposing Cairns distribution function.

In this article, modified Korteweg-de Vries equation (which involves cubic non-linearity) was derived to study non-linear ion acoustic waves in a plasma in which electrons follow the double spectral index distribution function. The double spectral index distribution successfully apes the distribution functions that have been frequently observed in space plasmas. The spectral index r moulds the distribution function at low energy and by increasing its value, flatness of the distribution enhances. The spectral index r can also have negative values due to which distribution becomes spiky at low energies. The index q, on the other hand, controls the shape of the tail of distribution function. It has been shown that propagation of the solitary structures gets significantly altered by the choice of the double spectral indices, namely, r and q. A comparison was also made, using the parameters of the auroral zone, between the quadratic and cubic non-linearities-driven non-linear structures and it was shown that the solitary structures form on a much shorter scale for cubic non-linearity compared to their quadratic counterpart. K E Y W O R D S(r, q) distribution, KdV equation, modified KdV, nonlinear ion acoustic waves, nonthermal electrons

In this paper, we have studied the propagation of non-linear ion-acoustic waves in a plasma comprising of (r, q)-distributed electrons and kappa-distributed positrons. We have investigated the effect of complete electron distribution profile on the propagation of small, as well as arbitrary, amplitude solitons (via pseudopotential technique) by using generalized (r, q) distribution, which exhibits a spiky and flat top nature at low energies and a super-thermal tail at high energies. Interestingly, for negative values of r, solitons are formed with both polarities, positive (compressive) and negative (rarefactive), separately within a small amplitude limit and exist simultaneously in an arbitrary amplitude limit. We also found that the propagation of solitons has been affected by the change in parameters r, q, positron concentration, and electron to positron temperature ratio. The results presented in this study add to the fundamental understanding of the complete profile of the electron distribution function, highand low-energy parts, and in the formation of compressive and rarefactive small and finite amplitude solitons in both space and astrophysical plasmas.

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