We investigate the dynamics of a kink in a damped parametrically driven nonlinear Klein-Gordon equation. We show by using a method of averaging that, in the high-frequency limit, the kink moves in an effective potential and is driven by an effective constant force. We demonstrate that the shape of the solitary wave can be controlled via the frequency and the eccentricity of the modulation. This is in accordance with the experimental results reported in a recent paper [Casic et al., Phys. Rev. Lett. 110, 168302 (2013)], where the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a time-dependent magnetic field has been studied.

• Received 23 October 2014

DOI:https://doi.org/10.1103/PhysRevE.91.032908