Targeted transfer of solitons in continua and lattices

We propose a robust mechanism of targeted energy transfer along a line, as well as on a surface, in the form of transport of coherent solitary-wave structures, driven by a moving, spatially localized external ac field ("arm") in a lossy medium. The efficiency and robustness of the mechanism are demonstrated analytically and numerically in terms of the nonlinear Schrödinger (NLS) equation, and broad regions of stable operation are identified in the model's parameter space. Direct simulations show that the driving arm can manipulate solitons equally well in a lattice NLS model. A salient feature, which is revealed by simulations and explained analytically, is a resonant character of the operation of the driving arm in the lattice medium, both integer and fractional resonances being identified. Numerical experiments also demonstrate that the same solitary-wave-transport mechanism works well in two-dimensional lattice media.