Nonlinear wave number shift and modulational instability for large amplitude waves in a relativistic magnetised plasma

Properties of large amplitude waves in a relativistic magnetised plasma are studied using the method of reductive perturbation. The plasma under consideration consists of warm adiabatic ions and isothermal warm electrons, under the influence of a magnetic field. A consideration of large amplitude waves demands study of the relativistic situation. In the present case both the electrons and ions are considered to be relativistic. A KdV equation is derived from which a nonlinear Schroedinger equation is deduced by further scaling. Lastly an expression is derived for nonlinear wave number shift, critical angle of propagation and the condition for modulational instability. This analysis is applicable to both laboratory and space plasmas. 18 refs., 2 figs