Summary: We establish the long-time stability of low-energy solitary waves in one-dimensional nonintegrable lattices with Hamiltonian \(H = \sum_{j\in {\mathbb Z}} \left(\frac{1}{2} p_j^2 + V(q_{j+1}-q_j)\right)\)with a general nearest-neighbour potential \(V\). As a corollary, we obtain a recurrence theorem related to numerical observations by Fermi, Pasta and Ulam.
Part III, ibid. 17, No. 1, 207–227 (2004; Zbl 1103.37049).