NONLINEAR-WAVE NUMBER SHIFT AND MODULATIONAL INSTABILITY FOR LARGE-AMPLITUDE WAVES IN A RELATIVISTIC MAGNETIZED PLASMA

Properties of large amplitude waves in a relativistic magnetised plasm a are studied using the method of reductive perturbation. The plasma u nder consideration consists of warm adiabatic ions and isothermal warm electrons, under the influence of a magnetic field. A consideration o f large amplitude waves demands study of the relativistic situation. I n the present case we consider both the electrons and ions to be relat ivistic. A KdV equation is derived from which a nonlinear Schrodinger equation is deduced by further scaling. Lastly we derive an expression for nonlinear wave number shift, critical angle of propagation and th e condition for modulational instability. Our analysis is applicable t o both laboratory and space plasmas.