A good approximation of modulated amplitude waves in Bose–Einstein condensates

• We explore the dynamics of BECs with scatter lengths varying periodically.
• Action and angle variables for singular systems are constructed.
• A good approximation for MAWs is obtained.

In this paper, we present a perturbation method that utilizes Hamiltonian perturbation theory and averaging to analyze spatio-temporal structures in Gross–Pitaevskii equations and thereby investigate the dynamics of modulated amplitude waves (MAWs) in quasi-one-dimensional Bose–Einstein condensates with mean-field interactions. A good approximation for MAWs is obtained. We also explore dynamics of BECs with the nonresonant external potentials and scatter lengths varying periodically in detail using Hamiltonian perturbation theory and numerical simulations.