Nonlinear wave modulation and stability criteria for strongly dispersive ion-acoustic waves

We have derived the Nonlinear Schrodinger Equation (NLSE) for strongly dispersive ion-acoustic plasma waves taking into consideration the electron inertia effect through the parameter Q (= m(e)/m(b), the ratio of electron to ion mass). In the present studies, the NLS equation is obtained by the modified reductive perturbation method and the derived equation is studied for the nonlinear wave modulation and the stability criteria. The parameter Q leads to higher dispersion compared to the case of electrons considered as Maxwellian. Consequently stronger nonlinearity comes into play for the studies of solitary wave propagation. In short it can be said that electron inertia effect modifies the nonlinear and dispersive coefficients of the NLS equation. The coefficient of the nonlinear term in the NLS equation turns to be complicated owing to the presence of electron mobility. A parametric range is obtained for angular frequency (omega) and the wave number k in order to get the stable region. It is found that instability occurs for small values of k due to electron inertia effect, A progressive wave type of solution of the NLS equation is obtained and plotted numerically to observe the modulation of nonlinear wave structure. Also a steady state solution of the NLS equation is derived.