Solitary Alfvén Waves

We present the solitary Alfvén wave, an exact nonlinear solution of the ideal magnetohydrodynamic (MHD) equations, and construct a three-dimensional numerical model – an \emph{Alfvénon}. The model is characterized by an unperturbed far field, quasi-constant $\mathrm{\mid }\mathit{B}\mathrm{\mid }$, and open field-line topology. Direct MHD simulations of the Alfvénon demonstrate remarkable stability, confirming that it behaves as a nonlinear solitary Alfvénic solution under ideal MHD evolution.