International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 599-614
doi:10.1155/S0161171285000655

Study of nonlinear wave processes in plasmas using the formalism of a special Lorntz transformation for a space-independent fram

S. N. Paul,1 B. Chakraborty,1 and L. Debnath2

1Department of Mathematics, Jadavpur University, Calcutta 700032, India
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA

Received 11 May 1984; Revised 7 December 1984

Copyright © 1985 S. N. Paul et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.