Evolution of large amplitude Alfvén waves in the solar wind with β∼1

A new set of equations is obtained which describes evolution of finite amplitude, dispersive, elliptically polarized quasi‐parallel Alfvén waves, when the plasma and the wave amplitude satisfy the condition, |1‐C_S²/C_A²| < δB/B₀, where C_A and C_s are the Alfvén and the sound speed, respectively, and δB/B₀ is the Alfvén wave amplitude normalized to the background magnetic field. When this condition is satisfied, the sound wave as well as the right‐ and left‐hand polarized Alfvén waves are nearly all degenerated. The solar wind plasma is a typical medium for the obtained set of equations to apply, since the plasma β is high, and the solar wind Alfvén waves have large amplitude. Modulational instability of a circularly polarized parallel Alfvén wave is discussed.