# Seeking good parametrization of homoclinic solution

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!

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Can't you solve for $p=p(q)$ and use $q$ as the parameter? –  Hans Lundmark Sep 28 '12 at 6:35
I woke up and I had the same idea. Actually it is even better than that. Due to the structure of my perturbation I can eliminate integrals involving $p$ entirely using the relation and just use $q$. You suggested and excellent parametrization! –  Predrag Punosevac Sep 28 '12 at 15:07