Guiding-center soliton

We consider the behavior of solitons described by the nonlinear Schr\"odinger equation with periodic perturbation (not necessarily small) whose period ${\mathit{Z}}_{\mathit{a}}$ is much shorter than the characteristic period of the solitons, ${\mathit{Z}}_{0}$. The soliton behaves like the guiding-center motion of a charged particle in a magnetic field, smooth and adiabatic. However, when ${\mathit{Z}}_{\mathit{a}}$ approaches ${\mathit{Z}}_{0}$, resonances appear between the periodic perturbations and the characteristic frequencies of the solitons which induce the generation of dispersive waves and/or splitting of solitons.