The two‐dimensional dynamics of nonlinear ion‐acoustic waves in plasmas are considered. A new nonlinear equation is found which is valid for unmagnetized as well as magnetized plasmas. For exactly vanishing magnetic fields, the Kadomtsev–Petviashvili equation is recovered; for weak magnetic fields, however, the dynamics are qualitatively different from that equation, depending on amplitude. With increasing magnetic field, the new equation becomes similar (but not identical) to the Zakharov–Kuznetsov equation which was derived for very strong magnetic fields. The stability behavior of plane solitons propagating along the magnetic field is also discussed. The transition from stable to unstable behavior and some quantitative new results for the instability growth rates are presented.