In this thesis we discuss the evidence for scatter in g at right angles o two vortices in a head-on collision. The evidence is given in terms of the approximate solutions of the equations of motion or the Euler-Lagrange equations DiD^+^Wm2- 1) = 0, d,Fij + i/2(o*Djo - <f>(DJ<f>y) = 0 where D{ = (<9, — iA{) and F{j = d{Aj — djAi and (At(x),<ft(x)) describe the gauge potentials and Higgs fields respectively. The case A = 1 describes the case where there are no net forces on the vortices but we also extend the analysis to th e case o f a sm a ll net repulsive force between the corresponding static vortex configurations where A > 1. The ordinary differential equations, which result from th e ansatz for th e approximate solutions, are solved by Taylor series a t the origin and a sym p to tic series at infinity.