Dual perturbation expansion for a classical $\lambda {\varphi }^4$ field theory

We prove the existence of a strong coupling expansion for a classical $\lambda {\varphi }^4$ field theory in agreement with the duality principle in perturbation theory put forward in [M.Frasca, Phys. Rev. A 58, 3439 (1998)]. The leading order solution is a snoidal wave taking the place of plane waves of the free theory. We compute the first order correction and show that higher order terms do renormalize the leading order solution.