A study is made of nonlinear waves in plasmas using the formalism of a special Lorentz transformation for a space-independent frame, S ′ . This special transformation is used to transform the space-time dependent equations in a cold, relativistic, magnetized plasma to the S ′ frame. Then the transformed equations are employed to derive the expressions for the Lagrangian and the Hamiltonian in the S ′ frame. The Lagrengian and the Hamiltonian for a strong circularly polarized laser beam have also been obtained in the S ′ frame. The exact form of the nonlinear dispersion relation is derived for circularly polarized waves. Then the results for the frequency and the wave number shifts of these waves in a cold, magnetized relativistic plasma are obtained with some Discussion on the nature of the frequency shifts. Finally, numerical results are presented for the radiation of Nd-glass laser in dense plasmas.