Solitary wave interaction in a cold collisionless plasma

The interaction between two solitary waves in a cold collisionless plasma having different velocities has been studied using the multiscale expansion method. The propagation of nonlinear waves through a cold collisionless plasma is described by mKdV and KdV equations in(1 + 1) dimensions and mKP and KP equations in (2 + 1) dimensions for different orders of a small perturbation parameter under the same time and space scale transformations. The interacting system of equations are derived for mKdV and KdV equations as well as for mKP and KP equations. We have also analysed the interacting system of equations in (1 + 1 ) dimensions.