An Explicit Solution for Nonlinear Plasma Waves of Arbitrary Amplitude
  Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result of increasing contribution of harmonics and may be used in theoretical studies of processes involving nonlinear plasma waves. 
A. G. Khachatryan and S. S. Elbakian