Seeking good parametrization of homoclinic solution

Question

Could somebody quickly provide me with a good parametrization of the homoclinic solution $$\frac{p^2}{2}-\frac{q^2}{2}+\frac{q^3}{3}=0$$ of the system \begin{aligned} \dot{q}&=p\\ \dot{p}&=q-q^2 \end{aligned} I am trying to evaluate Melnikov function of the related perturbed system of ODEs. Thank you for your attention!