Soliton dynamics and interaction in a deterministic aperiodic nonlinear lattice

We perform a numerical study of the dynamical properties of solitons in a one-dimensional deterministic aperiodic nonlinear lattice. The lattice is described by a discrete nonlinear Schrödinger equation, where the aperiodicity enters through an on-site potential chosen according to the substitutionally generated Thue-Morse sequence. Rapidly moving solitons are shown to propagate with small dispersion and radiation if they have a phase-modulation wavelength corresponding to regions of small amplitudes in the Fourier spectrum of the on-site potential. Such solitons also remain essentially unchanged after collision. Furthermore, we show that, for slowly moving solitons, an effective particle model is useful in order to understand some of the dynamic behavior, e.g., trapping of the solitons around points where they experience a local extremum in energy. The relation between the width and energy of the solitons is also discussed.