Solitary Wave Interactions of the Euler-Poisson Equations

We study solitary wave interactions in the Euler-Poisson equations modeling ion acoustic plasmas and their approximation by KdV n-solitons. Numerical experiments are performed and solutions compared to appropriately scaled KdV $n$-solitons. While largely correct qualitatively the soliton solutions did not accurately capture the scattering shifts experienced by the solitary waves. We propose correcting this discrepancy by carrying out the singular perturbation scheme which produces the KdV equation at lowest order to higher order. The foundation for this program is laid and preliminary results are presented.