Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Could somebody quickly provide me with a good parametrization for 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!

share|cite|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.