The solar atmosphere and solar wind are magnetically structured. The structuring can include tangential discontinuities, which can support surface waves. Such waves can be dispersive. This means that dispersion and nonlinearity can balance in such a way that solitary waves (or solitons) can result. This general point is illustrated by a two-dimensional nonlinear analysis which explicitly demonstrates the presence of long-wavelength solitary waves propagating on tangential discontinuities. If the waves are only weakly nonlinear, then they obey the Korteweg-de Vries equation and are true solitons.