  Charge migration is the electronic response that immediately follows
localized ionization or excitation in a molecule, before the nuclei have time
to move. It typically unfolds on sub-femtosecond time scales and most often
corresponds to dynamics far from equilibrium, involving multi-electron
interactions in a complex chemical environment. While charge migration has been
documented experimentally and theoretically in multiple organic and inorganic
compounds, the general mechanism that regulates it remains unsettled. In this
work we use tools from nonlinear dynamics to analyze charge migration that
takes place along the backbone of conjugated hydrocarbons, which we simulate
using time-dependent density functional theory. In this electron-density
framework we show that charge migration modes emerge as attosecond solitons and
demonstrate the same type of solitary-wave dynamics in both simplified model
systems and full three-dimensional molecular simulations. We show that these
attosecond-soliton modes result from a balance between dispersion and nonlinear
effects tied to time-dependent multi-electron interactions.%Our soliton-mode
mechanism, and the nonlinear tools we use to analyze it, pave the way for
understanding migration dynamics in a broad range of organic molecules.%For
instance, we demonstrate the opportunities for chemically steering charge
migration via molecular functionalization, which can alter both the initially
localized electron perturbation and its subsequent time evolution.
