Ion acoustic wave group dynamics near critical non-thermal parameter in non-thermal plasmas

Weakly nonlinear ion acoustic wave group dynamics at critical non-thermal parameter is investigated in the frame work of Gardner equation in non-thermal plasmas. Also the wave modulation due to self-interactions near the critical parameter is investigated by a nonlinear Schrödinger equation. The non-thermal parameter modifies the wave dispersion and the parameter space of wave modulation. At the boundary of this parameter space, the wave group dynamics is shown to be governed by a modified nonlinear Schrödinger equation. These equations are solved numerically with the help of a pseudo-spectral scheme and the solutions predict a wide class of nonlinear structures related to wave and wave group dynamics of the weakly nonlinear wave. The numerical solutions and the growth rate of the modified nonlinear Schrödinger equation confirm that the ion acoustic wave is modulationally unstable near the marginal state. The results are discussed in the context of astrophysical observations in auroral region