Genericity of the multibump dynamics for almost periodic Duffing-like systems

In this paper we consider ``slowly'' oscillating perturbations of almost periodic Duffing-like systems, i.e., systems of the form $\ddot u=u-(a(t)+\a(\o t))W'(u)$, $t\in$\R, $u\in$\R$^N$, where $W\in C^{2N}($\R$^N$,\R$)$ is superquadratic and $a$ and $\a$ are positive and almost periodic. By variational methods, we prove that if $\o>0$ is small enough then the system admits a multibump dynamics. As a consequence we get that the system $\ddot u=u-a(t)W'(u)$, $t\in$\R, $u\in$\R$^N$, admits multibump solutions whenever $a$ belongs to an open dense subset of the set of positive almost periodic continuous functions.