[en] A Korteweg de-Vries equation that is applicable to both the nonlinear magnetosonic fast and slow waves is derived from a two-fluid model with finite ion and electron pressures. As in the cold plasma theory, the fast wave has a critical angle θ_c. For propagation angles greater than θ_c (quasi-perpendicular propagation), the fast wave has a positive soliton, whereas for angles smaller than θ_c, it has a negative soliton. Finite β effects decrease the value of θ_c. The slow wave has a positive soliton for all angles of propagation. The magnitude of resonant ion acceleration (the υ_p x B acceleration) by the nonlinear fast and slow waves is evaluated. In the fast wave, the electron pressure makes the acceleration stronger for all propagation angles. The decrease in θ_c due to finite β effects results in broadening of the region of extremely strong acceleration. It is also found that strong ion acceleration can occur in the nonlinear slow wave in high β plasmas. Possibility of unlimited acceleration of ions by quasi-perpendicular magnetosonic fast waves is discussed. (author)