A nonlinear proton distribution function that is an exact stationary solution of the nonlinear Vlasov equation and Maxwell's equations and which supports a single nonlinear transverse Alfv¿n (ion cyclotron) wave that is circularly polarized and nondisprsive is proposed for most of the observations during high-speed solar wind streams. This nonlinear distribution removes te strong Alfv¿n wave instability, inconsistent with the persistence of the observed proton distribution functions in high-speed streams, found by the linear stability analysis. Model temperature anisotropies and drift velocities of the two spatially inhomogeneous bi-Maxwellian components are consistent with typical proton velocity distributions measured in high-speed streams at 1 AU. Two derived relations for each of the wave number and the phase velocity of the wave are obeyed within experimental uncertainties by two typical proton measurements. Our model also predicts that the alpha particle bulk flow velocity exceeds the proton particle bulk flow velocity, as is observed.