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Transformation of nonlinear plasma equations from a lab frame S to the space-independent frame S' (both inertial) for an electromagnetic (EM) wave in an unbounded plasma reduces the nonlinear partial differential equations in S to ordinary nonlinear differential equations in S'. This relativistically correct transformation is used (1) to find the intensity induced precessional rotation of the polarization ellipse of vibration of an EM wave, (2) in the S-frame Lagrangian of the particles and field produced by them to derive the exact nonlinearly correct dispersion relation for a strong circularly polarized wave in a cold unmagnetized plasma, and (3) to rectify some much discussed differential equations obtained by Akhiezer and Polovin (1956) to study the evolution of longitudinal and transverse waves in a cold plasma.

Some Applications of Transformation to the Space?independent Frame in the Processes of Strong Radiation in Plasmas