Supersymmetric Skyrmions : Numerical Solutions

We consider the ${\cal N}=1$ Skyrme model and obtain supersymmetric skyrmion solutions numerically. The model necessarily contains higher derivative terms and as a result the field equation becomes a fourth-order differential equation. Solving the equation directly leads to runaway solutions as expected in higher derivative theories. We, therefore, apply the perturbation method and show that skyrmion solutions exist upto the second order in the coupling constant.