MODULATIONAL INSTABILITY OF 2 TRANSVERSE-WAVES IN A COLD-PLASMA

By Whitham's method of averaged Lagrangian developed by Dysthe, two coupled nonlinear Schrodinger equations are obtained for the evolution of the amplitude of two plane polarized transverse waves in a cold plasma, both propagating in the same direction. Relativistic corrections are included and amplitude-dependent frequency shifts are derived. It is found that two transverse waves are modulationally unstable. The relativistic terms play an important part in this instability. © 1979, Cambridge University Press. All rights reserved.