Modulational instability of ion acoustic waves in the presence of density gradients

Abstract

Using the Krylov–Bogoliubov–Mitropolsky method of perturbation for weak non-linearities, we study the modulational instability of ion-acoustic waves in a collisionless plasma in the presence of a density gradient. We find that the density gradient of second or higher order of perturbation does not effect the dispersion and the non-linearity coefficients in the non-linear Schrödinger equation.